cide with the number of keys struck until three keys are struck, then as 5, which stands in the units column of the period on the register is not greater than the red figure on the next crooked topped key, we have obtained the first root figure. Annexing the next period to the remainder of the first period, we have 533 as a new number from which to obtain the second root figure. The first root figure multiplied by 20=60, therefore place the index finger of the left hand on the red 6, and the index finger of the right hand on the red 0 of the tens and units column of the 533, and strike once; move the right hand finger to the red 2 of its column, strike 62; then to the 4 (all the time watching the figure in the next higher column on the register, and counting the numbers struck), strike 61, and then to the 6, strike 66; then to the 8, strike 68, then move the right hand index finger back to the red 0, at the same time moving the left hand finger to the red 7, strike 70, then moving the right hand to the red 2, strike 72. Now having struck seven even numbers, to coincide with the seven standing on the register in the next higher column than the one on which the keys were struck, we observe the remainder which is 64, and as 64 is not greater than 74, the next even number, the second root figure has been obtained.
Annexing another period to the remainder 64, we have 6440 as a number from which to obtain the third root figure. Multiplying the first two root figures (37) by 20, we have 740 as a starting point from which to begin striking the series of even numbers; use 74 as a trial divisor, and begin striking it on the tens and hundreds column of the number 6440, to find the next root figure. After striking the trial divisor five times, move the right hand finger one key towards the register, as it is apparent that the sixth succeeding even number is always ten greater than the one used as a starting point. We find that not until the trial divisor has been struck 8 times, does the number of strokes coincide with the figure in the next higher column on the register, when the remainder being smaller than the trial divisor, 8 is the third root figure; therefore, we strike the red 0 in the units column of the 6440, and each succeeding bent top key towards the register, and coming to the last one, begin again on the same red 0 key and strike it and the next two succeeding bent keys, making 8 strokes in all, because 8 is the root figure found by using the trial divisor. 456 now appears as the remainder. Annexing the next period we have 45627 as a number from which to obtain the fourth root figure. 378, the root figures already obtained, multiplied by 20 equals 7560. Taking 75 as a trial divisor, we strike 6 times before the number of strokes coincide with the next higher figure (do not drop the right hand finger one key towards the register after the fifth stroke, as when obtaining the third root figure, because 10 added to 7560 would not change either of the figures of the trial divisor), then place the finger on the red 6 in the next column to the right, because 6 is the next figure to the trial divisor, and strike 6 times, because 6 is the root figure obtained by using the trial divisor (drop one key towards the register after the fifth stroke), then strike 6 times in rotation on the series of bent keys of the units column in the usual manner, when the root, 3786, will appear, with the remainder, 231, standing to the right.
Method where the first period on the left is greater than 25. To obtain the first root figure, strike the red 00 in the tens and units columns of the highest period, and then 02, 04, 06, 08, 10, 12, etc., until the number of strokes coincide with the figure in the next higher column on the register, and the remainder standing in the column in which the keys are struck is not
