There can't be many people around who actually worked with Professor Hartree on the Manchester differential analyser; I'm one, so perhaps it's reasonably appropriate that I should open the discussion on Dr. Croaken's paper. But let me first say a few words about Hartree himself, to whom the entire credit for bringing the differential analyser to Britain is due.
I had the great good fortune to be accepted as an undergraduate into the Honours School of Mathematics at Manchester in 1932 (yes - over 60 years ago), when the two professors were Mordell (Pure) and Hartree (Applied): both first-class mathematicians and both excellent teachers who took their Honours students very seriously indeed. I've remained grateful to them all my life. Hartree, who was born in 1897, became interested in computation at an early age; during the 1914-18 war, as a very young man, he worked in the Ordnance Board on gunnery, calculating shell trajectories and range tables: all done on hand-operated mechanical desk calculating machines which was the only computing equipment then available.
He first made his name in the late 1920s and early 1930s in the field of atomic structure. Mathematically this is all about solving partial differential equations and his great contribution was to develop methods by means of which actual structures could be worked out with an amount of effort which, though large, was possible to contemplate - again, remember, on hand-operated desk machines. Typically he did masses of this work himself: he was a first-class computer, of an intensely practical sort, meaning that his interest was always in physical problems and his methods were always aimed at giving results only to the number of significant figures that had meaning for the physics but which could be guaranteed to be correct to that number. I recall his once telling me that getting the solution to one (important) problem took him 400 hours of hand computing. This would all have been done on a little Brunsviga, his favourite machine.
It was the possibility of using the differential analyser to compute atomic structures that fired Hartree's imagination when he heard of Bush's machine and stimulated him first to build the Meccano model (with Arthur Porter) and then to raise the money needed to have a full-sized, fully engineered machine built for Manchester. Ironically, scarcely any atomic structure work was ever done on the machine; but it was used to get numerical solutions of a great variety of problems in general physics and engineering. An early application in electrical engineering was reported in a paper to the IEE by Hartree and Porter in 1938 on ... transients on a distortionless transmission line. Almost for his own entertainment Hartree, who was a great railway enthusiast, used it to calculate running times for real trains, hauled by real steam locomotives (Royal Scots) on real track, the west coast main line from Euston to Carlisle.
The machine was taken over by the Ministry of Supply in 1939 for what would now be called defense work - meaning, of course, weapons-related work and I joined the team there in 1940, working under Hartree. For any problem that could be reduced to the numerical integration of ordinary differential equations, and that covers a very great deal, the machine was the most powerful tool available anywhere at that time. Everything we did carried a security classification and of course nothing could be published during the war years. After the war Hartree wrote a consolidated account, but this just disappeared into the Ministry of Supply archives and so far as I know has never been seen since. We did a lot of work on radar, particularly on anomalous propagation, and, perhaps rather surprisingly, on heat flow in materials for which the thermal properties varied with temperature, this having a bearing on steel production: something on this was published later.
I think, after these 50 years or so, I can risk mentioning one calculation which you may find interesting. At one stage we were asked by a very distinguished physicist if we could tackle a non-linear parabolic partial differential equation and give him the numerical solution as a function of time. He was very careful not to give us any indication of the origin of the problem, but assured us that it was very important and that he could get formal authorisation at whatever level we needed for whatever effort we should need to expend. We did it, and it took a team of three, working under Hartree' s very active direction, not much under a year. Naturally we speculated among ourselves on the physical problem, and Hartree got it right: it concerned the separation of U235 from U238 by a diffusion process. The plant was being built at Oak Ridge, Tennessee, the equilibrium production rate could be determined fairly easily but there was no other way to find how long it would take to reach equilibrium, and they reckoned that Hartree was the man to do the job. Now, of course, it would be a trivial calculation for a personal computer but that's after a scarcely believable technological revolution; things were very different in 1943.
Just a final comment. If you'11 forgive the apparent bias, setting up he machine for a new problem was real man's work. It was a matter of joining up a whole lot of steel shafts - 3/8", I think - with couplings and keying gears on to these by means of set screws - a sort of super-Meccano, really; everything was covered with oil, and it was highly desirable to wear a boiler suit. And, of course, the decoration of the basement of the Schuster Building in which it was housed was in the best Victorian tradition of brown and white lavatory tiling.
