61 



ard unit of length as heretofore shown, forming a simulta- 

 neous measure of force and time in space. 



But now while all our measures above examined, and 

 which are based upon the elements of linear dimension, 

 have been referred to the decimal system of subdivision, 

 there remains yet to be considered the propriety of 

 attempting the introduction of this system of subdivision 

 into the admeasurement of angular magnitude, in which 

 the unit is fixed by nature in the circumference to radius 

 unity. 



As a periodical function, the year was by the ancient 

 Egyptians typified in form of a circle, under the emblem of 

 a serpent with its tail in its mouth ; and the division of this 

 circle into 360 degrees probably owes its institution to the 

 first rude estimate of 360 days to the solar year, while its 

 subdivision into months was obtained from the nearest 

 whole number of 12 lunations of 30 days each contained 

 in it. 



The division of the circumference into 360 equal parts or 

 degrees once accomplished, the next step in the business of 

 angular admeasurement was made by taking the chord as 

 linear measure of the arc it subtended ; and as the radius, 

 which may be assumed unity, is itself the chord of the 

 sixth part of the circumference, the arc whose linear mea- 

 sure is 1 contains 60 degrees, or is already an example of a 

 unit divide^, into this number of equal parts, and hence the 

 origin of the sexagesimal scale yet adhered to in the arith- 

 metic of angular magnitude. 



Whatever motive may have led to the division of the 

 day and the night each into a number twelve of parts cor- 

 responding to the division of the year into months, it obvi- 

 ously necessitated an immediate attention to the rule, that 

 if a magnitude be divided into a certain number of equal 

 parts, and that number be afterwards doubled, the parts 

 themselves must be halved in magnitude, so as not to dis- 

 turb the equality. In so doing, as one degree is the 3 ^th 



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