Page:Methods of Operating the Comptometer (1895).djvu/36



Before trying to extract square root, practice division on at least fifty examples, employing those having one, two, and also five figures in the divisor.

The simplest way to extract square root on the Comptometer is to act on the principle that in the series of odd numbers, 1, 3, 5, 7, 9, etc., the square of the number of terms always equals the sum of all the terms.

Thus: In the series 1, 3, 5, 7, 9, 11, 13, we have seven terms, and find that the sum of these terms is 49, and that the square of seven, the number of terms, is also 49.

Strike on the keys the number to be operated on, so that it will appear on the register of the machine, and separate it by the pointers above the register into periods of two figures each from the right.

strike the red 0 key in the units column of the highest period, and each succeeding key towards the register in that column which has a bent top. until the figure in the tens column of that period indicates the number of key strokes, and the figures in the units column indicate an amount not greater than the red figure on the next key to be struck. (This simply amounts to dividing by the series of number of which 1 is the starting point and 2 the common difference.) The figure which now stands in the highest column of the register (the column which was the tens of the first period) is the first root figure, and the figure in the next column to the right is the remainder of the first period.

To the remainder of the first period annex the next period on the right for a new number from which to obtain the second quotient figure. Multiply the root figure already obtained by 20. If this amount is less than the number composed of the remainder and the next period, use it as a starting point at which to begin striking the series of even numbers according to the red figures, and strike it and each succeeding even number (example, 4×20=80-82-84-86-88, etc.) until the number of even numbers struck coincide with the figure on the register in the column next higher than the highest key struck, and the figures in the column in which the keys are struck indicates an amount not greater than the next even number to be struck. If the first root figure multiplied by 20 is as large or larger than the minuend, the second root figure is 0; therefore annex one more period to the remainder and proceed to find the third root figure.

Proceed same as with the second, except that there are two or more root figures to be multiplied by 20.

to find each root figure the same as in the method of dividing by three or more numbers, after which strike each of the keys which represent the rest of the even numbers to be struck, the number of times required as indicated by the quotient figure obtained by the trial divisor.

$$\sqrt{14334027}$$. After striking 14334027 on the machine and pointing off, we find that 14 is the highest period. Striking the red 0 in the units column of that period, then each succeeding key having a crooked top, we find that the figure in the tens column of that period on the register does not coin-