720 THE RAMSDEN DIVIDING ENGINE. 



The late George Smith proposed to read 150 for 140, aud 75 for 70.* 

 Sayce and Bosanquet assert that "There is no foundation for this, ex- 

 cept the pre-couceived idea that the circle ought to be divided into 360o. 

 The numbers are imprinted on the clay with great clearness according 

 to the sexagesimal notation." [Montlily Notices^ R. A. S., 1880.) 



REASONS FOR DIVIDING THE CIRCLE INTO 360 DEGREES. 



On the other hand, we have the generally accepted statement that 

 the Egyptians divided the circle into 360° from the sun's annual course 

 or according to the number of days, dividing the year into 12 months, 

 and each month into 30 days and allotting 1^ to each day with an inter- 

 calary month every C years. 



The Greeks divided each month into three periods of ten days each. 



It will be remembered that the Jewish year contained only 354 days. 



It is not definitely known how the astrolabes of Hipparchus (second 

 century b. c.) and Ptolemy (second century A. D.) were divided; prob- 

 ably these graduated circles contained 360<^. It is stated that the par- 

 allactical instrument used by Copernicus (1473-1543), and by which he 

 measured altitudes, had its limb divided by equal divisions that were 

 the subtenses of 3' 49", 137 each. If an error of only 4".l was made in 

 measuring this instrument, and if 3'.45" was the correct reading it 

 would indicate that each quarter of the circle was divided into 1,440, 

 or each sixth of the circle into 960 equal parts. 



Many writers believe that the number 360 was selected from the fact 

 that it admits of a great many aliquot parts, such as 2, 3, 4, 5, C, 8, 

 and 9. 



It has occurred to me as not an unreasonable conjecture that the 

 origin of the sexagesimal system may have resulted in some way from 

 the fact that the circumference of the circle is divided into six equal parts 

 by chords exactly equal to the radius in length. I do not remember to 

 have seen this theory advanced by any previous writer. 



The earliest records indicate that each day was divided into six parts. 



In a recent paper on " Chaldean Astronomy," by Dr. Christopher 

 Johnson, of Johns Hopkins University (p. 141), he asserts that ''in the 

 earliest tablets the day is divided (at least for astronomical i)urposes) 

 into six watches — three day watches and three night watches." " In 

 the later tablets, however, we find a division of the day into 12 kaspu 

 or double hours, each kaspu being divided into 60 degrees or minutes." 



There is mention of an inscription on a tablet in "Western Asiatic 

 Inscriptions" (published by the British Museum, iii 51, 1), a translation 

 of which reads: "The sixth day of Nisan, day and the night were 

 balanced there were 6 kaspu of day and 6 kaspu of night." 



* " I am of opinion that the numbers under the month of Marchesvan, 140° and 70° 

 are errors in the Assyrian copy and should be 150^ and 75°." (George Smith's "Assy- 

 rian Discoveries," p. 407.) 



