In the preliminary notes it was shown that by mechanically adding two
lengths representing the logarithms of two numbers, we can obtain the
_product_ of these numbers; while by subtracting one log. length from
another, the number represented by the latter is divided by the number
represented by the former. Hence, using the C and D scales, we have the
RULE FOR MULTIPLICATION.—_Set the index of the C scale to one of the
factors on D, and under the other factor on C, find the product on D._
[Illustration: FIG. 10.]
Thus, to find the product of 2 × 4, the slide is moved to the right
until the left index (1) of C is brought over 2 on D, when under the
other factor (4) on C, is found the required product (8) on D. Following
along the slide, to the right, we find that beyond 5 on C (giving 10 on
D), we have no scale below the projecting slide (Fig. 10). If we imagine
the D scale prolonged to the right, we should have a repetition of the
earlier portion, but, as with the two parts of the A scales, the
repeated portion would be of tenfold value, and 10 on C would agree with
20 on the prolonged D scale. We turn this fact to account by moving the
slide to the left until 10 on C agrees with 2 on D, and we can then read
off such results as 2 × 6 = 12; 2 × 8 = 16, etc., remembering that as
the scale is now of tenfold value, there will be two figures in the
result. Hence, for those who prefer rules, we have the
RULE FOR THE NUMBER OF DIGITS IN A PRODUCT.—_If the product is read with
the slide projecting to the_ LEFT, ADD THE NUMBER OF THE DIGITS IN THE
TWO FACTORS; _if read with the slide to the_ RIGHT, _deduct 1 from this
sum_.