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
Placing the cursor to 114 on D, it is seen that the coinciding number
on A is 13. As the result is read off on the _left_ scale of A, the
number of digits will be (3 × 2) − 1 = 5, and the answer is read as
13,000. The true result is 12,996.
EX.—Find the square of 0·0093.
The cursor being placed to 93 on D, the number on A is found to be
865. The result is read on the _right_ scale of A, so the number of
digits = −2 × 2 = −4, and the answer is read as 0·0000865
[0·00008649].
_Square Root._—The foregoing rules suggest the method of procedure in
the inverse operation of extracting the square root of a given number,
which will be found on the D scale opposite the number on the A scale.
It is necessary to observe, however, that if the number consists of an
_odd_ number of digits, it is to be taken on the _left-hand_ portion of
the A scale, and the number of digits in the root = (N + 1)/(2), N being
the number of digits in the original number. When there is an even
number of digits in the number, it is to be taken on the _right-hand_
portion of the A scale, and the root contains _one-half_ the number of
digits in the original number.
EX.—Find the square root of 36,500.
As there is an _odd_ number of digits, placing the cursor to 365 on
the L.H. A scale gives 191 on D. By the rule there are (N + 1)/(2) =
(5 + 1)/(2) = 3 digits in the required root, which is therefore read
as 191 [191·05].
EX.—Find √(0·0098.)
Placing the cursor to 98 on the right-hand scale of A (since −2 is an
_even_ number of digits), it is seen that the coinciding number on D
is 99. As the number of digits in the number is −2, the number of
digits in the root will be (−2)/(2) = −1. It will therefore be read as
0·099 [0·09899+].
EX.—Find √(0·098).
The number of digits is −1, so under 98 on the left scale of A, we
find 313 on D. By the rule the number in the root will be (−1 +1)/(2)
= 0, and the root is therefore read as 0·313 [0·313049+].
EX.—Find √(0·149.)
As the number of digits (0) is _even_, the cursor is set to 149 on the
right-hand scale of A, giving 386 on D. By the rule, the number of
digits in the root will be (0)/(2) = 0, and the root will be read as
0·386 [0·38605+].
Another method of extracting the square root, by which more accurate
readings may generally be obtained, is by using the C and D scales only,
with the slide inverted. If there is an _odd_ number of digits in the
number, the _right_ index, or if an even number of digits the _left_
index, of the inverted scale Ɔ is placed so as to coincide with the
number on D of which the root is sought. Then with the cursor, the
number is found on D which coincides with the same number on Ɔ, which
number is the root sought.
EX.—Find √(22·2.)
Placing the left index of Ɔ to 222 on D, the two equal coinciding
numbers on Ɔ and D are found to be 4·71.
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