First, the number 49.3724 is examined in a counter called the _Logarithm-In-Out counter_, and the position of the decimal point is determined, giving the _characteristic_ of the logarithm. The number 49.3724 has the characteristic 1. Next, 4 successive divisions are performed, in which the 4 divisors are (1) the first digit of the number, (2) the first 2 digits of the quotient, (3) the first 3 digits of the next quotient, and (4) the first 4 digits of the subsequent quotient; thus, 4.93724/4 = 1.23431 1.23431/1.2 = 1.02860 1.02860/1.02 = 1.00843 1.00843/1.008 = 1.00043 For simplicity we have kept only 6 digits, although the machine, of course, would keep 23. It is interesting to note that the machine is able to sense digits and thus determine the 4 divisors; this is an arithmetical and numerical process and one that cannot be done in ordinary algebra. We now have: log₁₀ 49.3724 = 1 + log₁₀ 4 + log₁₀ 1.2 + log₁₀ 1.02 + log₁₀ 1.008 + log₁₀ 1.00043 To compute log₁₀ 1.00043 to 21 decimals we use ( _h_² _h_³ _h_⁴ _h_⁵ _h_⁶ ) log₁₀_e_ · (_h_ - ————— + ————— - ———— + ————— - —————) ( 2 3 4 5 6 ) with _h_ = 0.00043. Only 6 terms of the series relation are needed. For, the error is less than _h_⁷/7, which is less than 10⁻²¹/7, since _h_ < ¹/₁₀₀₀. The machine uses the series relation in the form log₁₀ (1 + _h_) = {([{(_c_₆_h_ + _c_₅)_h_ + _c_₄}_h_ + _c_₃]_h_ + _c_₂)_h_ + _c_₁}_h_ where _c_₁ = _M_, _c_₂ = -_M_/2, _c_₃ = _M_/3, ···, and _M_ = log₁₀__e_= 0.434294···. The 6 values of the _c_’s are also stored in the machine. When any logarithm is to be computed, the sum of the characteristic, of the 4 logarithms of the successive divisors, and of the first 6 terms of the series relation gives the logarithm. The maximum time required is 90 seconds. AN APPRAISAL OF THE CALCULATOR The IBM Automatic Sequence-Controlled Calculator at Harvard is a landmark in the development of machines that think. Its capacity for many problems for which it is suited is far beyond the capacity of a hundred human computers. Speed