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
The foregoing method being an inversion of the rule for multiplication,
is easily remembered and is generally advised. Another plan is, however,
preferable when a series of divisions are to be effected with a constant
divisor—_i.e._, when _b_ in (_a_)/(_b_) = _x_ is constant. In this case
1 on the scale is set to the index and the pointer set to _b_; then if
any value of a is brought to the pointer, the quotient _x_ will be found
under the index.
_Combined Multiplication and Division_, as (_a_ × _b_ × _c_)/(_m_ × _n_)
= _x_, can be readily performed, while cases of continued multiplication
evidently come under the same category, since _a_ × _b_ × _c_ = (_a_ ×
_b_ × _c_)/(1 × 1) = _x_. Such cases as _a_/(_m_ × _n_ × _r_) = _x_ are
regarded as (_a_ × 1 × 1 × 1)/(_m_ × _n_ × _r_) = _x_; while (_a_ × _b_
× _c_)/(_m_) = _x_ is similarly modified, taking the form (_a_ × _b_ ×
_c_)/(_m_ × 1) = _x_. In all cases the expression must be arranged so
that there is _one more factor in the numerator_ than _in the
denominator_, _1’s being introduced as often as required_. The simple
operations of multiplication and division involve a similar disposition
of factors, since from the rules given it is evident that _m_ × _n_ is
actually regarded as (_m_ × _n_)/(1), while (_m_)/(_n_) becomes in
effect (_m_ × 1)/(_n_). It is important to note the general
applicability of this arrangement-rule, as it will be found of great
assistance in solving more complicated expressions.
As with the ordinary form of slide rule, the factors in such an
expression as (_a_ × _b_ × _c_)/(_m_ × _n_) = _x_ are taken in the
order:—1st factor of numerator; 1st factor of denominator; 2nd factor of
numerator; 2nd factor of denominator, and so on; the 1st factor as _a_
being set to the index, and the result _x_ being finally read at the
same point of reference.
EX.—(39 × 14·2 × 6·3)/(1·37 × 19) = 134.
Commence by setting 39 to the index, and the pointer to 1·37; bring
14·2 to the pointer; pointer to 19; 6·3 to the pointer, and read the
result 134 at the index.
It should be noted that after the first factor is set to the fixed
index, the _pointer_ is set to each of the _dividing_ factors as they
enter into the calculation, while the _dial_ is moved for each of the
_multiplying_ factors. Thus the dial is first moved (setting the first
factor to the index), then the pointer, then the dial, and so on.
_Number of Digits in the Result._—If rules are preferred to the plan of
roughly estimating the result, the general rules given on pages 21 and
25 should be employed for simple cases of multiplication and division.
For combined multiplication and division, modify the expression, if
necessary, by introducing 1’s, as already explained, and subtract the
sum of the denominator digits from the sum of numerator digits. Then
proceed by the author’s rule, as follows:—
_Always turn dial to the_ LEFT; _i.e._, _against the hands of a watch_.
Public-domain text, read in full here on John Shaqi.
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