1896-97-] COUNTING AND TIME RECKONING, 315 



clinch, or part where the whole is tightened. As may be easily imagined, 

 before this happened, the knots became extremely complicated. It was 

 the duty of persons in every province called Quipucamayus, or keepers of 

 the historical Quipos, to preserve by these string records the memory of 

 public events, and there were public buildings filled with these threads.* 

 According to Dr. Brinton this method of recording events and of count- 

 ing and distinguishing their sheep is still in use around Lake Titicaca, 

 the sex and other characteristics being indicated by different colours. f 



Dr. Peacock gives an interesting account of how time is recorded by 

 means of Mexican hieroglyphics. He says that they had only distinct 

 characters for i, 20, 400 and 8,000, yet by a peculiar process of com- 

 bination they were able to express any number, i, was represented by 

 a small circle ; 20, by a standard shaped as a parallelogram ; 400 by a 

 feather, and 8000 by a purse, supposed to contain the same number of 

 grains of cocoa. By dividing the parallelogram or hieroglyphic for 20 

 into four squares, and giving each a separate colour, they were 

 able to represent 5, 10, 15, and by taking half a feather they 

 could express 200. Their usual method, however, of representing the 

 units from i to 19 was by so many small circles, and I believe they 

 had other and more direct ways of expressing their numerals. B}' 

 the system referred to above, the year 1897 would be given thus: — 



® Hi iPPRPPPPFRPPiRPP 000,000,000.000,000,00. 



The Assyrians and other Eastern nations which used cuneiform 

 characters expressed their numbers from i to 9 by upright strokes, 

 thus, I, by I ; 2, by n ; 3, V>y m ; 4, by '{' ; 5, by '//. and so on. 10 was 

 expressed by < ; 11, by <i ; 12, by <n , 20, by < < ; 50 was <**; 100 was 

 <i-; 1,000, <<i-; the year 1897 would be thus expressed 



_^IIII ^, < < < < < nil 



^IIII '^' <.<<< HI 



18 too 90 7 



Probably the simplest way of writing numbers is well seen in Baby- 

 lonian inscriptions, where from i to 99 are obtained by a repetition of 

 the vertical arrowhead v= i- and a barbed sign <— 10. When a smaller 

 number was put to the right of the sign for 100 (y-), it was added and, 

 what seems singular to us, when it is put to the left, it gives the 

 number of hundreds. Thus y- <= no, but < {•- = 1000. 



Among the peculiarities in the notation of the Ancient Egyptians 

 may be mentioned the following, that whereas the hieroglyphic charac- 

 ters were written from left to right, in the hieratic, or more modern 



* See "Westminster Review" vol. ix. 1820. 

 t Dr. Brinton, in "Science," January 24, 1896. 



