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### EarlyHistory

## Excerpt from letter to Jim Hailstone from Jack Howlett, 11 November, 1995

During the war, as I think you know, I was working in a small group headed by Hartree and using the Manchester differential analyser, a sort of mathematical job shop in Ministry of Supply. I suppose we could be called back-room boys, the back room being the basement of the old Physics building in the university, lined with brown and white Victorian lavatorial tiles. For the sort of thing it could do, integrating differential equations, the machine like it's Cambridge twin, was more powerful than anything else around, and we did all sorts of things with it, including quite a lot on radar - for Bernard Lovell, then a young PSO, for example.

One day Peierls, then at Birmingham, came along with a non-linear parabolic (diffusion type) partial differential equation, the origin of which he didn't reveal and very clearly wasn't going to, but made it equally clear that the need was serious. The asymptotic solution, a function of the space variable, was almost obvious but what he wanted was the time to get to within some specified closeness, boundary conditions were at the end of the space range, and it was non-linear so you couldn't combine elementary solutions, so it was quite a tedious task and in fact took several months - I can tell you more about it some time if you're interested. Mind you, any half-decent PC would now take a few minutes at most, but this was 50 years ago and there wasn't any PCs.

Naturally, we tried to guess what this was all about - it was obviously some kind of chemical plant: my suggestion was that it was for synthetic rubber. Hartree got it right: it was the uranium isotope separation plant (Oak Ridge), tho' of course we didn't know that. They just did not know the order of the time from start-up to equilibrium (it turned out to be weeks - we of course had been given the equation in dimensionless variables). What's extraordinary is that with the resources behind that project they came to us for the calculation.

That's Part One. Part Two is that, not long after we'd done this, Peierls came along again, with a member of the Tube Alloys team, a Dr Klaus Fuchs, this time with a problem whose origin was obvious from the mathematics - the shock wave from a very intense spherical explosion. Fuchs had done a lot of very complicated mathematics on this, involving a whole lot of multiple-index series. It wasn't the kind of thing that the DA would handle at all well and I took it on myself; I may as well pat myself on the back and say that I found a quite simple substitution that started the solution off (formally, there was a discontinuity at the origin) and avoided all Fuchs's series development. I carried on the numerical solution a bit, but it was clearly a massive task and Peierls took it back to America where they finished it on punched card machines.

Part Three is that in 1947 I had gone back to my pre-war job of tame mathematician in the LMS railway and Fuchs, whom I hadn't seen in the interim, to Harwell to head Theoretical Physics Division. He had taken on a collection of young people to do computing - on desk machines, of course, no computers in the present sense then. He wanted someone to look after them and asked me: I said I would and after all the paper work had been gone through arrived at Harwell as a PSO in the summer of 1948.

The point of this long story is that if it hadn't been for Peierls' involvement with Tube Alloys, and his knowing Hartree and what he could do (remember that Peierls came to Manchester in the 1930s as a refugee from the Nazis) it's unlikely I should have gone to Harwell, and (with all due modesty - it was largely my idea) there might very well never have been an Atlas Lab. And I shouldn't have had such an enjoyable and rewarding a career.