THE RAMSDEN DIVIDING ENGINE. 723 



BABYLONIAN SYSTEM OF DIVIDING THE CIRCLE. 



Ill a paj)er upon "Babylonian Astronomy," by Sayce and Bosanquet 

 {Monthly Notices Royal Astronomical Society, 1880, vol. XL, No. 3, ), relat- 

 ing to the tablets of the millennial period, from 2,000 b. c. to 1,000 b. c, 

 I find this statement : " The divisions which we find employed are 8, 

 12, 120, 240, 480 parts. It has been assumed that the division of the 

 circle into 360 parts was made by this ancient people. There is how- 

 ever no authority in the inscriptions for this assumption. It seems to 

 have been derived originally from Achilles Tatius, and the precou. 

 ceived idea thus incroduced appears to have caused even those most 

 conversant with the inscriptions to see the divisions of the circle into 

 360 in matters which do not involve it. 



THE MODERN DIVISION AN OUTGROWTH OF THE SEXAGESIMAL 



SYSTEM. 



" It is hardly doubtful that the division of the circle as practiced by 

 Ptolemy and in modern times was an outgrowth of the sexagesimal 

 system, but the latter does not contain the former. The numeration of 

 the inscriptions is by two methods, the sexagesimal and the decimal. 



" The decimal method is in all respects comparable with our own and 

 was used by j)refereiice in the Assyrian period. 



" In it words and signs were used which were precisely equivalent to 

 our "hundreds" and "thousands." 



"In the sexagesimal method the reckoning was the same as in the 

 decimal up to 60; 60 was 1 soss. The counting went on by multiples of 

 60 4- number over, up to 1 ner = 600. Then by ners + sosses -f num- 

 ber over, up to 1 saru = 3,000. 



"The numbers used are always taken in this way. There is no in- 

 stance of counting by 60, 360, 3,600. The foundation of the number 

 360 was not, therefore, a natural step in the sexagesimal arithmetic of 

 the inscriptions. 



TABLET FROM THE PALACE* OF SENNACHERIB. 



" The division of the circle into 480 parts is illustrated by a tablet 

 from the palace of Sennacherib (668-626 b. c.) in the British Museum, 

 written in Accadiau, which treats of the moon's position during a 

 month. The numbers of them or many of them are unintelligible or cor- 

 rupt. This is partly due to the fact that the tablet is a copy of an ancient 

 one, probably the date before 2,000 b. c; but there is amply sulficient 

 left to show that there was a real division of 480 parts, the moon's 

 mean daily motion being 16°, as it should be roughly, throughout the 

 intelligible portions," 



