From the PREFACE.
The ordinary slide-rule, or Gunters scale, invented many years ago, for approximation or a rough check on ordinary calculation, has been found of great utility. It is, however, unfitted for the more exact calculations of the engineer, architect, and actuary, and does not satisfy all the requirements of scientific investigation or of financial transactions.
The value of the slide-rule as a calculator depends upon the accuracy of its results, upon the rapidity with which those results can be found, upon the variety of its useful applications, and upon the small amount of mental and physical effort required in the solution of problems.
With any form of slide-rule the results are necessarily approximate, the degree of approximation depending upon the length of scales, the care observed in their manufacture, and the material used. With the ordinary construction and material it is not practicable to make such length of scales as will give results beyond the third place, which latter is frequently in doubt, the doubt being still further increased by the unequal shrinkage of the material of which it is made, usually boxwood. The ordinary rule in use is 12 inches long, with radii of n and 5^ inches, . the divisions of which are cut by hand, copying from a machinedivided plate. In the present instrument the radii are 60 and 30 feet, the divisions of which are printed directly from machine-divided plates. These plates contain over 33,000 divisions, calculated to seven places of decimals from Babbage,s tables by using a common multiplier, every line being subjected to correction for error of screw and temperature variation, so that possibly every line centre is within .0001 inch of its true place. The plates contain over 17,000 engraved figures. The work was executed by W. F. Stanley, of London, upon a dividing-machine made expressly for this rule, the diamond point used for cutting the divisions being moved by a screw of 50 threads per inch, reading by micrometer to .000001 inch. It was a work requiring much time, care, and skill. The framework of this rule is of metal throughout, therefore not injuriously affected by variations in temperature nor moisture, no time, pains, or expense having been spared to make the instrument in every way reliable; the scales, being of great length, will give results correctly to four, and usually to five, places of figures, sufficient to satisfy nearly every requirement of the professional and business man. A knowledge of its use is readily acquired. The rules following a1e general, simple, and easily remembered. After once becoming familiar with the movements results are obtained with almost incredible rapidity; ordinary calculations, and complicated formulae involving roots and powers, being solved with nearly equal facility....