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
It is sometimes useful to remember that although we usually set the
slide to the rule, we can obtain the result equally well by setting the
rule to the slide. Thus, bringing 1 (or 10) on D to 2 on C, we find on
C, _over_ any other factor, _n_ on D, the product of 2 × _n_. But note
that the slide and rule have now changed places, and if we use rules for
the number of digits in the result, we must now deduct 1 from the sum of
the digits in the factors, when the _rule projects_ to the _right of the
slide_.
With the ordinary 10 in. rule it will be found in general that the
extent to which the C and D scales are subdivided is such as to enable
not more than three figures in either factor being dealt with. For the
same reason it is impossible to directly read more than the first three
figures of any product, although it is often possible—by mentally
dividing the smallest space involved in the reading—to correctly
determine the fourth figure of a product. Necessarily this method is
only reliable when used in the earlier parts of the C and D scales.
However, the last numeral of a three-figure, and in some cases the last
of a four-figure, product can be readily ascertained by an inspection of
the factors.
EX.—19 × 27 = 513. Placing the L.H. index of C to 19 on D, we find
opposite 27 on C, the product, which lies between 510 and 515. A glance
at the factors, however, is sufficient to decide that the third figure
must be 3, since the product of 9 and 7 is 63, and the last figure of
this product must be the last figure in the answer.
EX.—79 × 91 = 7189.
In this case the division line 91 on C indicates on D that the answer
lies between 7180 and 7190. As the last figure must be 9, it is at once
inferred that the last two figures are 89.
When there are more than three figures in either or both of the factors,
the fourth and following figures to the right must be neglected. It is
well to note, however, that if the first neglected figure is 5, or
greater than 5, it will generally be advisable to increase by 1 the
third figure of the factor employed. Generally it will suffice to make
this increase in one of the two factors only, but it is obvious that in
some cases greater accuracy will be obtained by increasing both factors
in this way.
CONTINUED MULTIPLICATION.—To find the product of more than two factors,
we make use of the cursor to mark the position of successive products
(the value of which does not concern us) as the several factors are
taken into the calculation. Setting the index of C to the 1st factor on
D, we bring the line of the cursor to the 2nd factor on C, then the
index of C to the cursor, the cursor to the 3rd factor, index of C to
cursor, and so on, reading the final product on D under the last factor
on C. (Note that the 1st factor and the result are read on D; all
intermediate readings are taken on C.)
Public-domain text, read in full here on John Shaqi.
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