BABYLONIA AND EGYPT 27 



once sixty plus four 

 once sixty plus twenty-one 

 once sixty plus forty 

 twice sixty plus one, etc., 



necessarily implying the representation of 60 by 1 in the second 

 place. 



In a table of cubes, the perfect cube 4096 is represented similarly 

 by 1 8 16, that is 1 X 60 2 + 8 X 60 + 16 = 4096. The origin 

 of this sexagesimal system has been ingeniously attributed to the 

 blending of two civilizations, one possessing a system based on 10, 

 the other a system based on 6, - - a combination suggested by the 

 command of the Persian king that the Ionian troops wait 60 

 days at the bridge over the Ister; by the splitting of the river 

 by Cyrus into 360 rivulets, etc. Fractions were employed to a 

 limited extent with denominators 60, and 3600 (= 60 X 60). 

 The great step of completing the number system by a character 

 for zero seems not to have been successfully made, though there 

 are indications of an approach to it in later Babylonian times. 

 There is evidence of a mystical or magical use of numbers. Each 

 god, for example, was designated by a number from 1 to 60 ac- 

 cording to his rank. 



A rational system of weights and measures was introduced, 

 the unit of weight depending on that of length, as in the modern 

 metric system. 



BABYLONIAN ASTRONOMY. In connection with astronomical 

 observations the Babylonians invented a method of measuring 

 time by means of the water clock or clepsydra. From a vessel 

 kept full, water was allowed to escape very slowly into a second 

 vessel in which it could be weighed. To equal weights of water 

 corresponded equal intervals of time. 



Starting the flow at the moment the upper edge of the sun 

 first appeared in the east and stopping as soon as the whole sun 

 was visible, the amount of water collected was compared with 

 that escaping from sunrise to sunrise, and the sun's diameter 

 thus determined as ?^y of its whole path in the sky. The time 



