The slide rule : $b a practical manual — John Shaqi
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
Here the number of digits in the dividend is −3, and in the divisor −1.
The difference is −2; but as the result is obtained with the slide to
the right, this result must be increased by 1, so that the number of
digits in the quotient is −2 + 1 = −1, giving the answer as 0·013.
If preferred, the result can be obtained in the manner referred to when
considering the multiplication of decimals. Thus, treating the above as
whole numbers, we find that the result of dividing 221 by 17 = 13, since
the difference in the number of digits in the factors, which is 1, is,
owing to the position of the slide, increased by 1, giving 2 as the
number of digits in the answer. Then by the rules for the division of
decimals we know that the number of decimal places in the quotient is
equal to 6 − 3 = 3, showing that a cypher is to be prefixed to the
result read on the rule.
As in multiplication, so in division, we have a
GENERAL RULE FOR NUMBER OF DIGITS IN A QUOTIENT.—_When the first
significant figure in the_ DIVISOR _is greater than that in the_
DIVIDEND_, the number of digits in the quotient is found by subtracting
the digits in the divisor from those in the dividend. When the contrary
is the case, 1_ IS TO BE ADDED _to this difference. When the first
figures are the same, those following must be compared._
ESTIMATION OF THE FIGURES IN A QUOTIENT.—The method of roughly
estimating the number of figures in a quotient needs little explanation.
EX.—3·95 ÷ 5340 = 0·00074.
Setting 534 on C to 3·95 on D we read under the (R.H.) index of C, the
significant figures on D, which are 74. Then 3·9 ÷ 5 is about 0·8 and
0·8 ÷ 1000 gives 0·0008 as a rough estimate.
EX.—0·00000285 ÷ 0·000197 = 0·01446.
Regarding this as 2·85 × 10^{−6} ÷ 1·97 × 10^{−4} we divide 2·85 by
1·97 and obtain 1·446. Dividing the powers of 10 we have 10^{−6} ÷
10^{−4} = 10^{−2}, so the decimal point is to be moved two places to
the left and the answer is read as 0·01446.
Another method of dividing deserves mention as of special service when
dividing a number of quantities by a _constant divisor_:—Set the index
of C to the divisor on D and over any dividend on D, read the quotient
on C.
For the division of a _constant dividend_ by a variable divisor, set the
cursor to the dividend on D and bring the divisor on C successively to
the cursor, reading the corresponding quotients on D under the index of
C. Another method which avoids moving the slide is explained in the
section on “Multiplication and Division with the Slide Inverted.”
CONTINUED DIVISION, if we can so call such an expression as
(3·14)/(785 × 0·00021 × 4·3 × 64·4) = 0·0688,
may be worked by repeating as follows:—Set 7·85 on C to 3·14 on D, bring
cursor to index of C, 2·1 on C to cursor, cursor to index, 4·3 to
cursor, cursor to index, 6·44 to cursor, and under index of C read 688
on D as the significant figures of the answer.
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