Taylor.] "^4 [Oct. 21, 



an employment which has been perpetuated throughout Europe and 

 America, to the present, in the smaller divisions of time and of the circle. 

 This scale is of course far too cumbrous in the range of its units to have 

 ever had a true notation, or to be ever possible as an actual system, 

 founded on its own radix. With its enormous complication of figures, it 

 would still require about y\ (or more than half ) of the places of the com- 

 mon system to express its values. It has been found very useful, how- 

 ever, in its limited application, both from the rapidity of its progressions, 

 and from the remarkablj' varied range of divisibility it permits. The 

 number 60 is divisible by 2, by 3, by 4, by 5, by 6, by 10, by 12, by 15, by 

 20, and by 30 ; and has indeed the greatest number of aliquot parts of any 

 number below 96. 



Our "minutes" and "seconds" of the degree and of the hour have 

 thus an Oriental origin. In India, however, from whence the scale was 

 derived, these divisions, as applied to time, had not the same value as with 

 us ; as there the day itself was divided into 60 parts, called guries (hours 

 of 24 minutes), each gurie into 60 parts, called polls (minutes of 24 of our 

 seconds), and lastly each poll into 60 mimiks, or twinklings of an eye 

 (four-tenths of a second). It is believed that this division of time is re- 

 tained by the Hindoos to the present day. They also employ a period of 

 60 years, as we do the century. 



In its astronomical application this scale has been found exceedingly 

 useful. The properties of the circle require that it should frequently be 

 divided into sixths, as well as into quarters ; the sixth being, as is well 

 known, the radial arc, or that whose chord is exactly equal to radius. The 

 zodiacal or ecliptic circle of the heavens had, from the earliest antiquity, 

 been divided into twelfths, a period representing approximately the move- 

 ment of the sun during one lunation. As this comprised very nearly 30 

 days, the "sign" became naturally divided into 30 degrees ; and this ex- 

 presses so closely the arc of the earth's orbit described in one mean solar 

 day, that when the earth is moving slowest (or at its aphelion), it falls but 

 three minutes within one degree, and when it is moving fastest (or at its 

 perihelion), it exceeds the degree by only a single minute. The radial 

 arc of two " signs," or 60 degrees, suggested its own subdivisions. Hence 

 was derived the table of 60 seconds to the minute, 60 minutes to the de- 

 gree, and 60 degrees to the sextant — 6 of these completing the circle. 

 This system, answering so well the requirements of various division, was 

 introduced from India into the Alexandrian school by the illustrious 

 Ptolemy,"" who did so much toward giving astronomy a scientific form. 

 The sexagenary scale has never, however, been computed by any other 

 than a denary radix. It must excite surprise, therefore, that the Hindoo 

 notation of the scale was nqt also introduced by Ptolemy at the same 



♦Although the sexagesunal arithmetic is commonly ascribed to Ptolemy, it is probably 

 an Eastern invention. The Indians, to this day, employ the sexagesimal division of 

 time" {Edinburgh Encydoiiedia, art. "Arithmetic"). 



