ii s. v. APRIL e, 1912.] NOTES AND QUERIES.
271
ARITHMETIC AMONG THE ROMANS :
THE ABACUS.
(11 S. v. 108, 173.)
CONVENIENT accounts of the Roman abacus and of the way in which " all whole numbers from 1 to 9,999,999 and the duo- decimal fractions of the as in common use " were represented will be found in Dr. James Gow's ' Short History of Greek Mathe- matics ' (Camb. Univ. Press. 1884) and in Dr. F. Hultsch's article ' Abacus ' in the first volume of Wissowa's edition of Pauly's ' Real-Encyclopadie der classischen Alter- tumswissenschaft ' (1894). The abacus con- tained a series of grooves in which buttons were made to slide up and down. The seven grooves in which units, tens, hundreds, thousands, &c.. to millions were marked were divided into upper and lower parts : the lower in each case contained four buttons (counting as 1, 10, 100, &c., in their respective grooves) ; the buttons in the upper part counted as 5, 50, 500, &c. In indicating numbers the buttons were pushed to the centre of the groove. When remaining at the ends, they were dead. Thus, starting at the right hand of the seven columns, the one in which units were marked, 1 to 4 would be denoted by pushing 1 to 4 buttons in the lower part of the column towards the middle. If 5 was to be marked, the four lower buttons would be pushed back to the foot and the one button in the upper part advanced. Six would be marked by keeping the upper button as in 5, and advancing one of the four lower buttons. When 10 was reached, the buttons in the unit column would be pushed back, and one of the lower buttons in the 10-column advanced. Simple addition and subtraction would be performed by marking one number on the abacus, carrying the other in one's head, and then altering the abacus to denote the result. It is not clear how more complicated pro- cesses were performed. Multiplication and division might be reduced to a series of additions and subtractions. Dr. Gow sug- gests that the use of the abacus may have been combined with'finger symbolism ; Dr. Hultsch, that the numbers may have been written in columns marked out on a board strewn with sand, or represented by means of inscribed counters. Surprise at what may seem cumbersome methods will be miti- gated if we remember that the Romans had
no interest in arithmetic as a mathematical
study, but looked on it solely as a means of
counting money. Mr. Boffin, who could not
read or write, calculated sums by a method
of his own. I have been told that there are
many small Neapolitan shopkeepers in the
same position. EDWAKD BENSLY.
A full description of the Chinese abacus will be found in my ' Things Chinese,' where both the abacus itself and the modus operandi are described. As each step is taken in the calculation the abacus shows the result of that step, but not the process by which the step is taken, as is done with figures ; each succeeding step obliterates the signs of the one preceding. For example, to show how the tiling is done in China (and the process must be very much the same wherever the abacus is used), take the simplest sum possible, just to show the principle 2 + 2 - 1 x4-=-2. Two of the balls are pushed up against the central bar to represent 2. Then for the addition two more. This is the first step, and the result is 4. Then for the subtraction, push back one of the balls, and the result of this next step is 3. For the multiplication by 4, one ball in the next row is pushed up against the bar, as that row represents tens, and one of the balls on the unit row is pushed away, thus showing the result 12. To divide, the 10 ball is not required, and is pushed away ; one only of the unit balls is retained, and one of the balls above the bar, which represents five, is brought up to the bar, for 5 and 1 are 6, the result of dividing 12 by 2. This is the principle of the whole working, no matter how com- plicated it may be. J. DYER BALL.
REGISTER TRANSCRIBERS OF 1602, &c. (11 S. v. 130, 216). The following extract from the minutes of Stepney Parish^Vestry throws some light on the mode of keeping and transcribing the registers in the early part of the seventeenth century. It also gives a contemporary record of the remunera- tion paid for this kind of work :
" At a vestrye holden the 11 th Decemb r 1613 in the vestrye in the Church It is agreed in maner f olowing ....
" Also yfc is agreed that whereas there is much of the Register vnrecorded as well for Christnings Mariages and Burialls where through much hurt may arise, that therefore Peter Wright If he like yt shall haue foure pounds for the full recording of all that is yet vnrecorded vnto the time of the death of Jhon Brockbancke late clerke and Keper of the Registrye, or if he shall make refusall thereof then the Churchwardens to
