The slide rule : $b a practical manualPickworth, Charles N. (Charles Newton)
Science
The slide rule : $b a practical manual
Pickworth, Charles N. (Charles Newton)
Slide-rule
For the number of figures in the result, we deduct the sum of the number
of digits in the several factors and add 1 for each time the slide
projects to the right, which in this case occurs once. There are 3 +
(−3) + 1 + 2 = 3 denominator digits, 1 numerator digit, and 1 is to be
added to the difference. Therefore there are 1 − 3 + 1 = −1 digits in
the answer, which is therefore 0·0688. The foregoing method of working
may confuse the beginner, who is apt to fall into the process of
continued multiplication. For this reason, until familiarity with
combined methods has been acquired, the product of the several
denominators should be first found by the continued multiplication
process, and the figures in this product determined. Then divide the
numerator by this product to obtain the result.
As the denominator product will be read on D, we may avoid resetting the
slide by bringing the numerator on C to this product and reading the
result on C _over_ the index of D. The slide and rule have here changed
places; hence if rules are followed for the number of figures in the
result, 1 must be added to the difference of digits, when the _rule
projects_ to the _right of the slide_.
The author’s method of recording the number of times division is
performed with the slide to the right is by vertical memorandum marks,
thus |. The full significance of these memo-marks will appear in the
following section.
For a rough calculation to fix the decimal point, in this example we
move the decimal points in the factors, obtaining
(3)/(0·8 × 2 × 4 × 6) = (3)/(40) = 0·075.
THE USE OF THE UPPER SCALES FOR MULTIPLICATION AND DIVISION.
Many prefer to use the upper scales A and B, in preference to C and D.
The disadvantage is that as the scales are only one-half the length of C
or D, the graduation does not permit of the same degree of accuracy
being obtained as when working with the lower scales. But the result can
always be read directly from the rule without ever having to change the
position of the slide after it has been initially set. Hence, it
obviates the uncertainty as to the direction in which the slide is to be
moved in making a setting.
When the A and B scales are employed, it is understood that the
left-hand pair of scales are to be used in the same manner as C and D,
and so far the rules relating to the latter are entirely applicable. But
in this case the slide is always moved to the right, so that in
multiplication the product is found either upon the left or right scales
of A. If it is found on the left A scale, the rule for the number of
digits in the product is found as for the C and D scales, and is equal
to the _sum of the digits in the two factors, minus 1_; but if found on
the right-hand A scale, the number of digits in the product is equal to
the sum of the digits in the two factors.
Public-domain text, read in full here on John Shaqi.
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