Page:Notes and Queries - Series 9 - Volume 11.djvu/371

 9*8. XI. MAY 9, 1903.] NOTES AND QUERIES.

363

word myriad (in its original sense of ten thousand), and the punctuation of the figures by fours, instead of by threes.

An example will best explain. Let us take for the purpose the number of seconds of time that have elapsed in the world's history up to the present, according to the Bible chronology, which is denoted by a row of twelve figures or, better still, the number of permutations in the ordinary pack of fifty-two playing-cards, in sets of thirteen cards, which is represented by a row of twenty-two figures. This latter number, with the usual punctuation, is as follows : 3,954,242,643,91 l,239,680,000,and in theFrench notation is "Three sextillions, nine hundred and fifty-four quintillions, two hundred and forty -two quadrillions, six hundred and forty-three trillions, nine hundred and eleven billions, two hundred and thirty-nine millions, six hundred and eighty thousand." The same number in the English notation is " Three thousand nine hundred and fifty-four trillions, two hundred and forty -two thousand six hundred and forty - three billions, nine hundred and eleven thousand two hundred and thirty-nine millions, six hundred and eighty thousand." Both take the same number of words to express. In the pro- posed new way the number would be punctu- ated as follows : 39,5424,2643,9112,3968,0000, and be notated : "Thirty-nine quintillions, five thousand four hundred and twenty-four quadrillions, two thousand six hundred and forty-three trillions, nine thousand one hundred and twelve billions, three thousand nine hundred and sixty-eight myriads." If the last four figures were 4321, instead of being ciphers, the continuation of the nota- tion would be "four thousand three hundred and twenty-one" in the ordinary way.

The main difficulty in reading a large number from figures is the ascertaining of the correct significance of the first characters on the left. Once they are understood, the rest follows easily and naturally. The present grouping gives no direct indication, in either the French or English system, of what these characters are; whereas in the proposed new way they are identified at once by the follow- ing rule : The groups to the right name the figures to the left. Thus, in the latter punctu- ated example there being five groups cut off, the first figures to the left (39) are quintillions. If there had been seven groups, they would have been septillions, three groups trillions, and so on. Nothing can be simpler. By it any row of figures may be tackled and named at once, without hesitation, even if met with for the first time in a paper publicly read out.

There are several additional advantages in this proposed system. In the first place, by the punctuation in fours the number of cha- racters contained in large numbers can be much more rapidly ascertained, as will be seen by reference to the two examples above. Next, it embraces thousands by single numbers, as well as hundreds and tens, in naming the higher steps. And the notation takes a rather less number of words to express

It is true that if the English system adopted the punctuation by sixes, some of its defects would be overcome. But to be of assistance to the eye (punctuation's main province), six figures in each step is too long an interval. What is gained in the rapid reaching of the significance of the first figures is lost in the confusion within the steps themselves. The proper punctuation for the English system would be 3,954;242,643;911,239;680,000, using semicolons as well as commas ; but that method at once stands condemned, because where several numbers occur together there would be confusion, especially in technical works. No punctuation, however, would ever get over the confused impression carried to the mind in the notation (when unassisted by the figures as well) by having in each of the steps hundreds, &c., coming both before and after thousands "two hundred and forty-two thousand six hundred and forty- three billions."

To sum up the suggested way a myriad has four ciphers (1,0000), a billion eight ciphers (1,0000,0000), a trillion twelve ciphers (1,0000,0000,0000), a quadrillion sixteen ciphers, and so on. Every quantity is punctuated in fours. The various steps embrace tens, hun- dreds, and thousands, by single numbers only.

The study of figures always brings up regret at the universal choice of the decimal system. If our semi-civilized forefathers instead of using both hands together for their counting, whereby they arrived at the number ten on the fingers had just gone a step higher and employed the two hands in com- bination, whereby the number thirty-five would have been reached, they would have conferred an inestimable benefit on their posterity, by giving us the senary scale, instead of the decimal, with an immense and incalculable savingof labour in our arithmetic. J. S. McTEAK.

MERRY TALES. (See 9 th S. viii. 297, 380; ix. 324 ; xi. 84.)

' Tales and Quicke Answeres? LX. 4 Of him that sought his asse and rode on his backe.' This is No. 55 in Poggio.