1·73 × 10^4 × 3·78 × 10^3 = 1·73 × 3·78 × 10^7.
Setting 1 on C to 1·73 on D, we read, under 3·78 on C, the result of
the simple multiplication, as 6·54. Multiplying by 10^7 moves the
decimal point 7 places to the right, and the answer is 65,400,000.
If it is required to find a series of products of which one of the
factors is _constant_, set 1 on C to the constant factor on D and read
the several products on D, under the respective variable factors.
If the factors are required which will give a constant _product_ (really
a case of division), set the cursor to the constant product on D. Then
obviously, as the slide is moved along, any pair of factors found
simultaneously under the cursor line on C, and on D under index of C,
will give the product. A better method of working will be explained when
we deal with the inversion of the slide.
It is sometimes useful to remember that although we usually set the
slide to the rule, we can obtain the result equally well by setting the
rule to the slide. Thus, bringing 1 (or 10) on D to 2 on C, we find on
C, _over_ any other factor, _n_ on D, the product of 2 × _n_. But note
that the slide and rule have now changed places, and if we use rules for
the number of digits in the result, we must now deduct 1 from the sum of
the digits in the factors, when the _rule projects_ to the _right of the
slide_.
With the ordinary 10 in. rule it will be found in general that the
extent to which the C and D scales are subdivided is such as to enable
not more than three figures in either factor being dealt with. For the
same reason it is impossible to directly read more than the first three
figures of any product, although it is often possible—by mentally
dividing the smallest space involved in the reading—to correctly
determine the fourth figure of a product. Necessarily this method is
only reliable when used in the earlier parts of the C and D scales.
However, the last numeral of a three-figure, and in some cases the last
of a four-figure, product can be readily ascertained by an inspection of
the factors.
EX.—19 × 27 = 513. Placing the L.H. index of C to 19 on D, we find
opposite 27 on C, the product, which lies between 510 and 515. A glance
at the factors, however, is sufficient to decide that the third figure
must be 3, since the product of 9 and 7 is 63, and the last figure of
this product must be the last figure in the answer.