Set cursor to 4·32 on A, and move the slide until 1·63 is found
simultaneously under the cursor on B and on D under 1 on C; bring
cursor to 1 on C; 4·32 on C to cursor, and _over_ 3·64 on D read 9·65
on C. (Note that in this case it is convenient to read the answer on
the _slide_; see page 22). From the slide rule we know ∛(4·32) = about
1·6; this into 4·32 is roughly 3; 3·64 × 3 is about 10, showing the
answer to be 9·65.
Similarly products of the form _a_ × _b_^{⁴⁄₃} are best dealt with as
_a_ × _b_ × ∛_b_.
Factorising expressions sometimes simplifies matters, as, for instance,
in _x_^4 − _y_^4 = (_x_^2 + _y_^2)(_x_^2 − _y_^2). Here, working with
the fourth powers involves large numbers and the troublesome
determination of the number of digits in each factor; but squares are
read on the rule at once, the number of digits is obvious, and, in
general, the method should give a more accurate result. Take the
expression, D_{1} = ∛((D^4 − _d_^4)/(D)) giving the diameter D_{1} of a
solid shaft equal in torsional strength to a hollow shaft whose external
and internal diameters are D and _d_ respectively. Rearranging as D_{1}
= ∛(((D^2 + _d_^2)(D^2 − _d_^2))/(D)) and taking, as an example, D = 15
in. and _d_ = 7 in., we have D^2 + _d_^2 = 274 and D^2 − _d_^2 = 176;
hence D_1 = ∛((274 × 176)/(15)) = ∛(3210) = 14·75 in.
_Reversed Scale Notation._—With expressions of the form 1 − _x_, or 100
− _x_, it is often convenient to regard the scales as having their
notation reversed, _i.e._, to read the scale backwards. When this is
done the D scale is read as shown on the lower line—
Direct Notation 1 2 3 4 5 6 7 8 9 10
D Scale
Reversed Notation 9 8 7 6 5 4 3 2 1 0
The new reading can be found by subtracting the ordinary reading from 1,
10, 100, etc., according to the value assigned to the R.H. index, but
actually it is unnecessary to make this calculation, as with a little
practice it is quite an easy matter to read both the main and
subdivisions in the reversed order. Applications are found in plotting
curves, trigonometrical formulæ, etc.