Among the problems that have been placed on the machine successfully are: solving the _differential equation_ of a _trajectory_ (see Chapter 5) and solving 32 _linear simultaneous equations_ in 32 _unknowns_ (see Supplement 2). In the second case, the routine tapes were designed to apply equally well to 11 to 100 linear equations in 11 to 100 unknowns. However, the machine can do a very broad class of problems, including, for example, computing a personal income tax. This calculation with all its complexity of choices cannot be placed on any of the mechanical brains described in previous chapters. The machine can, of course, be used to calculate any tables that we may wish to refer to. AN APPRAISAL OF THE CALCULATOR The Bell Telephone Laboratories general-purpose relay computer is probably the best mechanical brain made up to the end of 1947, in regard to the two important factors of reliability and versatility. Reliability The machine produces results that are practically 100 per cent reliable, for the machine checks each step before taking the next one. The checking principle is that exactly a certain number of relays must be energized. For example, as we said before, for each decimal digit there are 7 relays. Exactly 2 of these relays must be energized—no more, no less. If this does not happen, the machine stops at once without losing any numbers. Lights shine for many circuits in the control panel, and, if you compare what they ought to show with what they do show, you can usually find at once the location of the mistake. The trouble may be a speck of dirt between two contact points on a relay, and, when it is brushed away, the machine can go right ahead from where it stopped. According to a statement by Franz L. Alt, director of the computing laboratory at the Ballistic Research Laboratories, in December 1947, “the Bell machine had not given a single wrong result in eight months of operation, except when operators interfered with its normal running.” To guard against the risk of putting tapes in the wrong transmitters, the machine will check by the instructions contained in the tapes that the right tapes are in the right places. Time Required The time required to do problems on this mechanical brain is perhaps longer than on the others. The numbers are handled digit by digit on the input tapes, and the typewriter in the recorder moves space by space in order to get to the proper writing point. These are slow procedures. The speeds of numerical operation are: addition, ³/₁₀ second; multiplication, 1 second on the average; division, 2.7 seconds on the average; square root, 4.5 seconds on the average; logarithm, about 15 seconds. Staff