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

## The ‘Working Model’: Calvert’s classification

The initial loan of the Trainbox Differential Analyser to the Science Museum in May 1949 led Henry Calvert to pen the first of many letters to Douglas Hartree regarding the Museum’s collection and reclassification of the object. Calvert’s initial letter to Hartree was written on 1 June 1949. In it, Calvert asks if he ‘...should...be right in saying that this model was the first working Differential Analyser in [Britain]...’ and argues that if so, it deserved to ‘be preserved’.[9] This part of Calvert’s letter shares similarities with the mission statement of the Science Museum at the time, which called for the ‘...preservation of appliances which hold an honoured place in the progress of science’ (Lyons, 1978). Calvert’s wording ‘...should I be right…’ implies that he had a suspicion that the Trainbox he had just collected did not speak with the same voices as the original 1934 object. After the war, Calvert had sought a significant differential analyser item for the Science Museum’s collection, to help tell the story of analogue computing. Therefore, his attempt to clarify whether the object was ‘the first working differential analyser’ was an example of a curator checking the voice of the Trainbox to see if it could tell the story of differential analysis that he required. In 1949, the locations of other differential analysers – similar to the Hartree Differential Analyser and the Manchester Machine – were not well known, with many having been destroyed in the Second World War or kept in private collections (Froese Fischer, 2003). With this in mind, Calvert’s question regarding the provenance of the machine (‘Should I be right in saying that this model was the first working Differential Analyser in this country?’) takes on a new meaning. It appears to be an attempt to check whether the Trainbox could tell the same story of differential analysers as the part of the Manchester Machine he was also trying to collect. This is demonstrated further in the last paragraph of Calvert’s first letter, in which he requests that Hartree or one of his students visit the Museum to help ‘put it in working order’.[10]

### Figure 6

© Science Museum/Science & Society Picture Library

A closer view of the gearing, torque amplifiers, and glass wheel-and-disk integrating unit of the Trainbox model. Notice the lack of input and output tables

Hartree’s reply on 7 July 1949 reads as an attempt to clarify Calvert’s question of whether the object now in the Museum’s possession was the ‘...first working differential analyser [in Britain]’.[11] Hartree began by asserting that while there is a link between the collected object and the 1934 object, they were not the same and that ‘...more accurately, what is preserved is a portion – enough to illustrate all the main principles – of the first working one in Britain’.[12] This confirms the physical and instrumental changes that Hartree made to the object when he rebuilt it in 1947, giving his perspective on what the Trainbox was, relative to the original object: in his view it was no longer a ‘working model differential analyser’ as he had described the Meccano model in 1935 (Hartree and Porter, 1935). Hartree intended the Trainbox to be a working model *of a* differential analyser, which could demonstrate the principles of mechanical integration using a single, pre-programmed calculation, implying that he had moved the voice of the Trainbox away from the original voice of the Hartree Differential Analyser as a working machine.

### Figure 7

© Museum of Science and Industry

The Hartree Differential Analyser built by Douglas Hartree and Arthur Porter (pictured) in 1934

The technical differences between the two incarnations of the Hartree Differential Analyser are that the original object, built in 1934, had four distinct integrators, and an input and output table, while the Trainbox that Hartree rebuilt in 1947 had only a single integrator, and no input or output tables. The integrator was a central component of the original set of instrumental functions of the differential analyser, indicating what type of differential equations it could solve. Having four integrators meant that the original object could solve anything up to a second-order differential equation, while the single integrator on the Trainbox meant that it could only be used to demonstrate how first-order differential equations are integrated (as it had no output table). The difference in function between the two analysers is clear: one could resolve equations, the other could merely show how the object could resolve them. In a mathematical context, this difference in function is essential to understand in order to demonstrate why there were incongruities between the voices that Calvert ventriloquised through the Trainbox and those that it initially spoke with as a demonstration object. These differences relate to the number of the highest derivative present in the equation the object is resolving.

First-order differential equations are referred to as such because they only involve the first derivative (*y'*):

While there are many examples of first-order differential equations, one type that the Hartree Differential Analyser would have been used to resolve were those related to fluid mechanics (Hartree, 1946). The solutions to these equations helped mathematicians during the Second World War plot the trajectory of a plane more precisely, and therefore, calculate how best to hit them using ballistic anti-aircraft guns (Crank, 1947). The Trainbox, built after the war, was designed to demonstrate the first-order equation of tractive force as applied to railways. However, unlike the original 1934 object, the Trainbox could not resolve second-order equations. The difference between first- and second-order equations is that with the latter, the number of the highest derivative is of the second order (*y''*) rather than the first. An example of a second-order differential equation is:

An easier way to understand these second-order equations is to think of Newton’s Second Law of Motion, which establishes force (F) acting on mass (m) and the acceleration (a) that the force causes. Written as a second-order ordinary differential equation Newton’s Second Law is as follows:

The solution to this equation would demonstrate the velocity of an object and the law of motion when the force applied to an object depends on time. The first derivative (*v’*) relates to the velocity of an object where acceleration

is the rate of change of velocity (the derivative of velocity with respect to time). The second derivative (*x’’*) relates to velocity as the derivative of the position of the object with respect to time, such that it measures the derivative of the derivative of the position of the object with respect to time; it measures the change in metres per second, per second

These different derivatives (whether first- or second-order) would have been programmed into the Hartree Differential Analyser as mechanical inputs. The role of the integrator was to take these derivatives (programmed through the input table) and return the net change of the equation as a mechanical output. The solution to the equation was then expressed graphically via the output table. By contrast, the Trainbox could not be re-programmed with new first-order equations as it had no input or output tables. The removal of these pieces had led Hartree to pre-program the machine with a single equation to demonstrate how the variables could be seen to move through the mechanical components of the machine physically.

Understanding the importance of the integrator and the input and output tables in resolving differential equations helps to highlight the impact that their absence had on the voices of the rebuilt Trainbox. Hartree was aware of the different function of his rebuilt object without these tables, commenting that it could only ‘demonstrate the main principles of the original’.[13] Hartree’s choices when rebuilding the Trainbox changed the voices that it spoke with to audiences. However, because the Trainbox could ‘demonstrate the main principles of the original’ object, it still retained some instrumental functions of the original 1934 object. These similar instrumental aspects allowed Calvert to ventriloquise the voices Hartree had created with the 1934 object through the Trainbox to tell the particular story of differential analysis he needed, demonstrating that the voices of the object have multiple sources (Hawks, 1934, pp 411–444).

This process began on 14 July 1949, when Calvert received a letter from Hartree explaining that through his discussions with John Womersley, the first superintendent of the Mathematics Division at the National Physical Laboratory (NPL), he could confirm to Calvert that ‘[they would] probably want to keep their (full-size) d. a. for 3 or 4 years for institutional and training purposes’.[14] When it became clear that the Manchester Machine would not be available, Calvert used the object that he had in hand — the Trainbox — and began to ventriloquise the voices of the original object, so that the Trainbox could tell the story of a working differential analyser. He began this process with a loan request form sent to the Director of the Science Museum on 15 July 1949. The form stated that ‘Professor Hartree...offers to lend ** a** meccano model

**Differential Analyser to the Museum’ (emphases added).[15] The emphasised words reveal that Calvert understood that the Trainbox was a just a ‘portion of a differential analyser’. However, the rest of his loan request form demonstrates his attempts to ventriloquise the voices of the original object through the Trainbox. This is evident in how his description of the Trainbox changes from a model ‘of a’ Differential Analyser to:**

*of a*‘*This* meccano model *was the* first working Differential Analyser outside the U.S.A…after Prof. Bush had built the machine...Prof. Hartree made* this working model* of it, which would actually solve equations’ (emphases added).[16]

Calvert’s use of the demonstrative adjective ‘this’, as well as the words ‘was the’ when describing the object’s past, conflates the voices of the original Hartree Differential Analyser’s physical and instrumental functions (the working model differential analyser) with those of the Trainbox (the working model *of a* differential analyser). This conflation continued in the next sentence of the loan form, which described that Hartree had built this ‘working model’. This implies that what the Museum had was the object Hartree had built in 1934 which could ‘actually solve equations’.[17] Despite the incongruities that existed between the voices of the two objects, Calvert’s ventriloquism served to collapse the physical and instrumental gap between the functionality of the two objects, conflating them and presenting the original object and the Trainbox as the same thing. This is clear in Calvert’s next sentence which describes how ‘...*this* working model demonstrated the usefulness of the machine and as a result, a large one was constructed at Manchester University’ (emphasis added).[18]

Through this note, Calvert moved the voices of the Trainbox from being ‘a portion’ (as described by Hartree), through ‘the meccano model of a differential analyser’, and the ‘working model’ that Hartree built in 1934, to, finally, an object that served as a ‘proof-of-concept’ for the Manchester Machine. These alterations were made to allow Calvert to ventriloquise the voices of the Trainbox to tell the story of differential analysis that he wanted to tell. His attempts to ventriloquise the voices of the object are also clear in a letter sent to the Director of the Science Museum, in which he explained that ‘...the usefulness of the model to the Museum would be to enable us to show it in operation to demonstrate the principles... Hitherto we have only exhibited photographs of the Manchester Machine’.[19] In the same form, Calvert used the term ‘in operation’, which implied the Trainbox was a ‘working model’.[20] This contrasted with his use of the phrase ‘demonstrate the principles’ later in the form, which borrowed from Hartree’s original set of voices for the Trainbox.[21]

A more significant challenge that Calvert faced — beyond the incongruities between the original and ventriloquised voices of the object — was that the Trainbox had been broken down into components as part of the collection process in 1949. As a dismantled object, it could not speak with any of the voices he was trying to ventriloquise through it. To resolve this issue, Calvert wrote to Hartree again on 3 March 1950 to remind him of the offer to visit the Museum to ‘...put [the object] back in working order’.[22] Calvert’s request reflected the way in which he had changed the voices of the Trainbox with his description of ‘a Meccano model of the Differential Analyser’, supplanted by the statement in the following sentence that 'the *machine* is now installed in a case’ (emphasis added).[23] Calvert’s choice of the word ‘machine’ over ‘model’ appears not to be accidental here, but represents another way of transferring the physical and instrumental aspects of the original object (i.e. those relating to the physical form of the object and those relating to its function) to the Trainbox. This conclusion is reinforced in the rest of the sentence, which explains that ‘…the machine is now installed in a case and is ready to connect to the mains’.[24] The phrase ‘ready to connect to the mains’ demonstrates that although the object was missing an input and output table, which precluded it from being a ‘working model’, Calvert was still attempting to ventriloquise the voices of the original ‘working model’ analyser through the Trainbox.

When Hartree did eventually visit the Museum on 18 July 1950 (sudden bouts of sickness had prevented him twice previously from doing so), he spent two hours with Calvert showing him the different aspects of the Trainbox object and how each part functioned.[25] Based on the archival record available, this was the last interaction between Hartree and Calvert regarding the Trainbox until 1957, when a branch of the Institute of Physics in Manchester requested to borrow the object from the Science Museum. In the final letter that Hartree sent to Calvert on 5 April 1957, he regarded the ‘...meccano model differential analyser as entirely at the Museum’s disposal…’ and that the loan request from the Manchester Institute of Physics had been at his suggestion.[26] He also offered his services to visit the Museum to fix the model should it return with some minor damage.[27] However, Calvert never requested Hartree for help in repairing the differential analyser as Hartree died of heart failure on 12 February 1958 at Addenbrooke’s Hospital in Cambridge (Froese Fischer, 2003).[28]

The above analysis of the correspondence between Calvert, Hartree and the Director of the Science Museum demonstrates the various ways that Calvert attempted to ventriloquise the voices of the original object through the Trainbox. Calvert’s ventriloquy caused incongruities that lay dormant within the object as it passed into the care of future curators in the Museum. The voices that the Trainbox had spoken with through its accession documentation and correspondence, and the instrumental and physical stories it was used to tell when on exhibition, were not consistent with the actual object on display. When Jane Pugh (who worked with the Trainbox from 1973–74) used it to create the Museum’s new *Mathematics and Computers* gallery, she had to find a way of reconciling the ventriloquised voices of the analyser with the object in the Museum’s collection.

Component DOI: http://dx.doi.org/10.15180/181005/004