Part 8

Practise reading values by setting 1 on C to some value on D and reading under 2, 3, 4, etc., on C, checking the readings by mental arithmetic. To the same end, find squares, square roots, etc., comparing the results with the actual values as given in tables. Practise setting both slide and cursor to values taken at random. Aim at accuracy; speed will come with practice.

When in doubt as to any method of working, verify by making a simple calculation of the same form.

Follow the orthodox methods of working until entirely confident in the use of the instrument, and even then do not readily make a change. If any altered procedure is adopted, first work a simple case and guard carefully against unconsciously lapsing into the usual method during the operation.

Unless the calculation is of a straightforward character, time taken in considering how best to attack it (rearranging the expression if desirable) is generally time well spent.

In setting two values together, set the cursor to one of them on the rule, and bring the other, on the slide, to the cursor line.

In multiplying factors, as 57 × 0·1256, take the fractional value first. It is easier to set 1 on C to 1256 on D and read under 57 on C, than to reverse the procedure. When both values are eye-estimated, set the cursor to the second factor on C and read the result on D, under the cursor line.

In continuous operations avoid moving the slide further than necessary, by taking the factors in that order which will keep the scale readings as close together as possible.

SQUARES AND SQUARE ROOTS.

We have seen that the relation which the upper scales bear to the lower set is such that over any number on D is its square on A, and, conversely, under any number on A is its square root on D, the same remarks applying to the C and B scales on the slide. Taking the values engraved on the rule, we have on D, numbers lying between 1 and 10, and on A the corresponding squares extending from 1 to 100. Hence the squares of numbers between 1 and 10, or the roots of numbers between 1 and 100, can be read off on the rule by the aid of the cursor. All other cases are brought within these ranges of values by factorising with powers of 10, as before explained.

The more practical rule is the following:—

To Find the Square of a Number, set the cursor to the number on D and read the required square on A under the cursor. The rule for

The Number of Digits in a Square is easily deducible from the rule for multiplication. If the square is read on the left scale of A, it will contain twice the number of digits in the original number less 1; if it is read on the right scale of A, it will contain twice the number of digits in the original number.

EX.—Find the square of 114.

Placing the cursor to 114 on D, it is seen that the coinciding number on A is 13. As the result is read off on the left scale of A, the number of digits will be (3 × 2) − 1 = 5, and the answer is read as 13,000. The true result is 12,996.

EX.—Find the square of 0·0093.

The cursor being placed to 93 on D, the number on A is found to be 865. The result is read on the right scale of A, so the number of digits = −2 × 2 = −4, and the answer is read as 0·0000865 [0·00008649].

Square Root.—The foregoing rules suggest the method of procedure in the inverse operation of extracting the square root of a given number, which will be found on the D scale opposite the number on the A scale. It is necessary to observe, however, that if the number consists of an odd number of digits, it is to be taken on the left-hand portion of the A scale, and the number of digits in the root = (N + 1)/(2), N being the number of digits in the original number. When there is an even number of digits in the number, it is to be taken on the right-hand portion of the A scale, and the root contains one-half the number of digits in the original number.

EX.—Find the square root of 36,500.

As there is an odd number of digits, placing the cursor to 365 on the L.H. A scale gives 191 on D. By the rule there are (N + 1)/(2) = (5 + 1)/(2) = 3 digits in the required root, which is therefore read as 191 [191·05].

EX.—Find √(0·0098.)

Placing the cursor to 98 on the right-hand scale of A (since −2 is an even number of digits), it is seen that the coinciding number on D is 99. As the number of digits in the number is −2, the number of digits in the root will be (−2)/(2) = −1. It will therefore be read as 0·099 [0·09899+].

EX.—Find √(0·098).

The number of digits is −1, so under 98 on the left scale of A, we find 313 on D. By the rule the number in the root will be (−1 +1)/(2) = 0, and the root is therefore read as 0·313 [0·313049+].

EX.—Find √(0·149.)

As the number of digits (0) is even, the cursor is set to 149 on the right-hand scale of A, giving 386 on D. By the rule, the number of digits in the root will be (0)/(2) = 0, and the root will be read as 0·386 [0·38605+].

Another method of extracting the square root, by which more accurate readings may generally be obtained, is by using the C and D scales only, with the slide inverted. If there is an odd number of digits in the number, the right index, or if an even number of digits the left index, of the inverted scale Ɔ is placed so as to coincide with the number on D of which the root is sought. Then with the cursor, the number is found on D which coincides with the same number on Ɔ, which number is the root sought.

EX.—Find √(22·2.)

Placing the left index of Ɔ to 222 on D, the two equal coinciding numbers on Ɔ and D are found to be 4·71.