MULTIPLICATION

We will start with a very simple example:

Example 1:  2 * 3 = 6



To prove this on the slide rule, move the slider so that the 1 at the
left-hand end of the C scale is directly over the large 2 on the D scale
(see figure 1). Then move the runner till the hair-line is over 3 on the
C scale. Read the answer, 6, on the D scale under the hair-line. Now,
let us consider a more complicated example:

Example 2:   2.12 * 3.16 = 6.70



As before, set the 1 at the left-hand end of the C scale, which we will
call the left-hand index of the C scale, over 2.12 on the D scale (See
figure 2). The hair-line of the runner is now placed over 3.16 on the C
scale and the answer, 6.70, read on the D scale.


METHOD OF MAKING SETTINGS


[This 6 inch rule uses fewer minor divisions.]

In order to understand just why 2.12 is set where it is (figure 2),
notice that the interval from 2 to 3 is divided into 10 large or major
divisions, each of which is, of course, equal to one-tenth (0.1) of the
amount represented by the whole interval. The major divisions are in
turn divided into 5 small or minor divisions, each of which is one-fifth
or two-tenths (0.2) of the major division, that is 0.02 of the
whole interval. Therefore, the index is set above

  2 + 1 major division + 1 minor division = 2 + 0.1 + 0.02 = 2.12.



In the same way we find 3.16 on the C scale. While we are on this
subject, notice that in the interval from 1 to 2 the major divisions are
marked with the small figures 1 to 9 and the minor divisions are 0.1 of
the major divisions. In the intervals from 2 to 3 and 3 to 4 the minor
divisions are 0.2 of the major divisions, and for the rest of the D (or
C) scale, the minor divisions are 0.5 of the major divisions.

Reading the setting from a slide rule is very much like reading
measurements from a ruler. Imagine that the divisions between 2 and 3 on
the D scale (figure 2) are those of a ruler divided into tenths of a
foot, and each tenth of a foot divided in 5 parts 0.02 of a foot long.
Then the distance from one on the left-hand end of the D scale (not
shown in figure 2) to one on the left-hand end of the C scale would he
2.12 feet. Of course, a foot rule is divided into parts of uniform
length, while those on a slide rule get smaller toward the right-hand
end, but this example may help to give an idea of the method of making
and reading settings. Now consider another example.

Example 3a:  2.12 * 7.35 = 15.6



If we set the left-hand index of the C scale over 2.12 as in the last
example, we find that 7.35 on the C scale falls out beyond the body of
the rule. In a case like this, simply use the right-hand index of the C
scale. If we set this over 2.12 on the D scale and move the runner to
7.35 on the C scale we read the result 15.6 on the D scale under the
hair-line.

Now, the question immediately arises, why did we call the result 15.6
and not 1.56? The answer is that the slide rule takes no account of
decimal points. Thus, the settings would be