386 THE POPULAR SCIENCE MONTHLY. 



be needed, that the basis of the system of counting was not deter- 

 mined by theoretical considerations, but by the simple elementary fact 

 of the number of human digits being ten and not twelve* 



Nevertheless twelve has its turn as a favorite number ; we often 

 count by dozens, and the reason probably is that twelve admits of 

 being quartered as well as halved, which in many cases is an advan- 

 tage. Take the case of wine : a dozen bottles is a convenient quan- 

 tity to take as a standard, because a customer can order half the 

 standard number, or, if he needs a small quantity, the quarter of the 

 same ; in fact, twelve admits of being divided not only by two and 

 four, but also by three and 6ix, which for many purposes give it a 

 great advantage over ten, which can be divided only by two and five, 

 the latter division being rarely of any use. Hence the great divisibil- 

 ity of twelve is sufficient to mark it as a favorite number, but in the 

 most notable instance of its use — namely, as marking the number of 

 months in a year — we need some further explanation. The real 

 month — that is, the number of days between two successive full 

 moons — may be taken as measured by twenty-eight days. Thirteen 

 times twenty-eight makes three hundred and sixty four, or as nearly 

 as may be one year. Consequently, it would have been much more 

 nearly true to say that thirteen months make a year than twelve. 

 The explanation is to be found, I conceive, in the extremely awkward 

 character of the number thirteen ; it is what is called by mathema- 

 ticians a prime number ; that is to say, it admits of no division of 

 any kind : had there been thirteen months in the year, the half-year 

 and the quarter alike could not have been reckoned by months, and 

 consequently twelve, which, as already explained, is one of the most 

 convenient of numbers in the matter of divisibility, was encouraged 

 and permitted to usurp the place, which, in all strictness, belonged to 

 its next-door neighbor. 



There is a somewhat parallel case with regard to the division of 

 the circle into 3G0 degrees. The ancient Chinese mathematicians 

 divided the circle into 365£ degrees, corresponding to the length of 

 the year, or 3G5£ days, which number, though not exact, is very 

 near the truth. f But this division of the circle is practically in- 

 tolerable ; it would throw mathematicians into despair ; consequently 

 the number 360, which admits of being divided by 4, by GO, by 90, 

 and by many other numbers, ursurped the place which the Chinese 

 righteously assigned to the awkward number which Nature suggested. 



I now pass on to the consideration of the number seven. It has 



* The device of place, according to which the suoeessivc figures in writing numbers 

 represent units, tens, hundreds, thousands, etc., as we proceed from right to left, is of 

 Indian origin. The Romans, with all their practical cleverness, did not discover this 

 6imple and ingenious device ; but they equally testify to the use of ten — or rather of fivo 

 and ten — as the basis of calculation by their notation of numbers I, V, X, L, G. 



f Biot, " Astronomie Physique," voL i, p. 69. 



