| log₁₀e · |  | h - | h² | + | h³ | - | h⁴ | + | h⁵ | - | h⁶ |  |
| 2 | 3 | 4 | 5 | 6 |
with h = 0.00043. Only 6 terms of the series relation are needed. For, the error is less than h⁷/7, which is less than 10⁻²¹/7, since h < ¹/₁₀₀₀. The machine uses the series relation in the form
log₁₀ (1 + h) = {([{(c₆h + c₅) h + c₄}h + c₃]h + c₂)h + c₁}h
where
c₁ = M, c₂ = -M/2, c₃ = 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.