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were “. . . and carry out instruction Potpan 15” the genuine input will have to be of form “. . . and carry out instruction 001101. . .1” where 001101. . .1 is the new number given to Potpan 15 in this particular job. This is a straightforward sorting and collating process.
It would be theoretically possible to do this rearrangement of orders within the machine. It is thought however that this would be unwise in the earlier stages of the use of the machine, as it would not be easy to identify the orders in machine form and popular form. In effect it would be necessary to take an output from the calculator of every order in both forms.
8. Scope of the Machine.
The class of problems capable of solution by the machine can be defined fairly specifically. They are those problems which can be solved by human clerical labour, working to fixed rules, and without understanding, provided that
(a) The amount of written material which need be kept at any one stage is limited to the equivalent of 5,000 real numbers (say), i.e. about what can conveniently be written on 50 sheets of paper.
(b) That the human operator, doing his arithmetic without mechanical aid, would not take more than a hundred thousand times the time available on the calculator, this figure representing the ratio of the speeds of calculation by the two methods.
(c) It should be possible to describe the instructions to the operator in ordinary language within the space of an ordinary novel. These instructions will not be quite the same as the instructions which are normally given to a computer, and which give him credit for intelligence. The instructions must cover every possible eventuality.
Let us now give real examples of problems that do and problems that do not satisfy these conditions.
Problem 1.— Construction of range tables. The complete process of range-table construction could be carried out as a single job. This would involve calculation of trajectories by small arcs, for various different quadrant elevations and muzzle velocities. The results at this stage would be checked by differencing with respect to other parameters than time. The figures actually required would then be obtained by interpolation and these would finally be rearranged in the most convenient form. All of this could in theory be done as a single job. In practice we should probably be wiser to do it in several parts in order to throw less responsibility on to the checking arrangements. When we have acquired more practical experience with the machine we will be bolder.
It is estimated that the first job of this kind might take one or two months, most of which would be spent in designing instruction tables. A second job could be run off in a few days.
Problem 2.— To find the potential distribution outside a charged conducting cube. This is a problem which could easily be tackled by the machine by a method of successive approximations; a relaxation process would probably be used. In relaxation processes the action to be taken at each major step depends essentially on the results of the steps that have gone before. This would normally be considered a serious hindrance to the mechanisation of a process, but the logical control of the proposed calculator has been designed largely with such cases in view, and will have no difficulty on this score. The
