If the rule for the number of digits in a product is used, it is necessary to note the number of times multiplication is effected with the slide projecting to the right. This number, deducted from the sum of the digits of the several factors, gives the number of digits in the product. Ingenious devices have been adopted to record the number of times the slide projects to the right, but some of these are very inconvenient. The author’s method is to record each time the slide so projects, by a minus mark, thus −. These can be noted down in any convenient manner, and the sum of the marks so obtained deducted from the sum of the digits in the several factors, gives the number of digits in the product as before explained. EX.—42 × 71 × 1·5 × 0·32 × 121 = 173,200. The product given, which is that read on the rule, is obtained as follows:—Set R.H. index of C to 42 on D, and bring the cursor to 71 on C. Next bring the L.H. index of C to the cursor, and the latter to 1·5 on C. This multiplication is effected with the slide to the right, and a memorandum of this fact is kept by making a mark −. Bring the R.H. index of C to the cursor and the latter to 0·32 on C. Then set the L.H. index of C to the cursor and read the result, 1732, on D under 121 on C, while as a slide again projects to the right, a second − memo-mark is recorded. There are 2 + 2 + 1 + 0 + 3 = 8 digits in the factors, and as there were 2 − marks recorded during the operation, there will be 8 − 2 = 6 digits in the product, which will therefore read 173,200 (173,194·56). For a very rough evaluation of the result, we note that 1·5 × 0·3 is about 0·5; hence, as a clue to the number of figures we have 40 × 70 × 60 = 3000 × 60 = 180,000. DIVISION. The instructions for multiplication having been given in some detail, a full discussion of the inverse process of division will be unnecessary. RULE FOR DIVISION.—_Place the divisor on C, opposite the dividend on D, and read the quotient on D under the index of C._ EX.—225 ÷ 18 = 12·5. Bringing 18 on C to 225 on D, we find 12·5 under the L.H. index of C. As in multiplication, the factors are treated as whole numbers, and the position of the decimal point afterwards decided according to the following rule, which, as will be seen, is the reverse of that for multiplication:— RULE FOR THE NUMBER OF DIGITS IN A QUOTIENT.—_If the quotient is read with the slide projecting to the_ LEFT, _subtract the number of digits in the divisor from those in the dividend; but if read with the slide to the_ RIGHT, ADD _1 to this difference_.[2] In the above example the quotient is read off with the slide to the right, so the number of digits in the answer = 3 − 2 + 1 = 2. EX.—0·000221 ÷ 0·017 = 0·013.