The degree of accuracy obtainable with the slide rule depends primarily
upon the length of the scale employed, but the accuracy of the
graduations, the eyesight of the operator, and, in particular, his
ability to estimate interpolated values, are all factors which affect
the result. Using the lower scales and working carefully the error
should not greatly exceed 0·15 per cent. with short calculations. With
successive settings, the discrepancy need not necessarily be greater, as
the errors may be neutralised; but with rapid working the percentage
error may be doubled. However, much depends upon the graduation of the
scales. Rules in which one or more of the indices have been thickened to
conceal some slight inaccuracy should be avoided. The line on the cursor
should be sharp and fine and both slide and cursor should move smoothly
or good work cannot be done. Occasionally a little vaseline or clean
tallow should be applied to the edges of the slide and cursor.
That the percentage error is constant throughout the scale is seen by
setting 1 on C to 1·01 on D, when under 2 is 2·02; under 3, 3·03; under
5, 5·05, etc., the several readings showing a uniform error of 1 per
cent.
A method of obtaining a closer reading of a first setting or of a result
on D has been suggested to the author by Mr. M. Ainslie, B.Sc. If any
graduation, as 4 on C, is set to 3 on D, it is seen that 4 main
divisions on C (40–44) are equal in scale length to 3 main divisions on
D (30–33). Hence, very approximately, 1 division on C is equal to 0·75
of a division on D, this ratio being shown, of course, on D under 10 on
C. Suppose √(4·3) to be required. Setting the cursor to 4·3 on A, it is
seen that the root is something more than 2·06. Move the slide until a
main division is found on C, which exactly corresponds to the interval
between 2 and the cursor line, on D. The division 27–28 just fits,
giving a reading under 10 on C, of 74. Hence the root is read as 2·074.
For the higher parts of the scale, the subdivisions, 1–1·1, etc., are
used in place of main divisions. The method is probably more interesting
than useful, since in most operations the inaccuracies introduced in
making settings will impose a limit on the reliable figures of the
result.
For the majority of engineering calculations, the slide rule will give
an accuracy consistent with the accuracy of the data usually available.
For some purposes, however, _logarithmic section paper_ (the use of
which the author has advocated for the last twenty years) will be found
especially useful, more particularly in calculations involving
exponential formulæ.