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
If of 2 figures, the number will be taken on the “tens” scale—_i.e._, on
the R.H. scale of A, using the L.H. index of C.
If of 3 figures, the number will be taken on the “hundreds”
scale—_i.e._, on the L.H. scale of A, using the R.H. index of C.
To determine the number of digits in cube roots it is only necessary to
note that when the number is pointed off into sections as directed,
there will be one figure in the root for every section into which the
number is so divided, whether the _first_ section consists of 1, 2, or 3
digits.
Of numbers wholly decimal, the cube roots will be decimal, and for every
group of _three_ 0s immediately following the decimal point, _one_ 0
will follow the decimal point in the root. If necessary, 0s must be
added so as to make up complete multiples of 3 figures before proceeding
to extract the root. Thus 0·8 is to be regarded as 0·800, and 0·00008 as
0·000080 in extracting cube roots.
EX.—Find ∛(14,000.)
Pointing the number off in the manner described, it is seen that there
are _two_ figures in the first section—viz., 14. Setting the cursor to
14 on the R.H. scale of A, the slide is moved to the right until it is
seen that 241 on the L.H. scale of B falls under the cursor, when 241 on
D is under the L.H. index of C. Pointing 14,000 off into sections we
have 14 000—that is, _two_ sections. Therefore, there are two digits in
the root, which in consequence will be read 24·1 [24·1014+].
EX.—Find ∛(0·162.)
As the divisional section consists of _three_ figures, we use the
“hundreds” scale. Setting the cursor to 0·162 on the L.H. A scale, and
using the R.H. index of C, we move the slide to the left until under the
cursor 0·545 is found on the L.H. B scale, while the R.H. index of C
points to 0·545 on D, which is therefore the cube root of 0·162.
EX.—Find ∛(0·0002.)
To make even multiples of 3 figures requires the addition of 00; we have
then 200, the cube root of which is found to be about 5·85. Then, since
the first divisional group consists of 0s, one 0 will follow the decimal
point, giving ∛(0·0002) = 0·0585 [0·05848].
_Cube Root (Inverted Slide Method)._—Another method of extracting the
cube root involves the use of the inverted slide. Several methods are
used, but the following is to be preferred:—_Set the_ L.H. _or_ R.H.
_index of the slide to the number on A, and the number on ᗺ (i.e., B
inverted), which coincides with the same number on D, is the required
root._
Setting the slide as directed, and using first the L.H. index of the
slide and then the R.H. index, it is always possible to find _three_
pairs of coincident values. To determine which of the three is the
required result is best shown by an example.
EX.—Find ∛(5,) ∛(50,) and ∛(500.)
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