C Y C 



CURVATURE radius. of t in any curre, irJtose equation is g/'ren. 

 Let x, y, and z represent the abscissa, ordinate, and curve, then 



Rad. = , * (rfa-beinsr constant - f '] ( 1 -\ ~-^) ' 



d^vd-y (hy \ d d* J 



Or Rad - = ^ bein& coustaut} = 



For the Curvature of Spirals see Spiral. 



CYCLE. 



A circulation of time between the returns of the same event. 



Cycle of the sun, a space of 28 years, in which time the days of the 

 month return again to the same days of the week, and the sun's place to 

 the same degrees of the Ecliptic on the same days, so as not to differ 1 

 in 100 years ; and the leap years return again in respect to the days of 

 the week on which the days of the months fall. To find it, add 9 to the 

 given year of Christ, and divide the sum by 28, and the quotient is the 

 number of cycles elapsed since his birth, and the remainder is the cycle 

 for the given year ; if nothing remain the cycle is 28. 



Cycle of the moon, or golden number, a revolution of 19 years, in which 

 time the conjunctions, oppositions, and all other aspects of the moon, 

 return on the same days of the months as they did 19 years before, but 

 about 1| hours sooner. To find it, add I to the given year of Christ, and 

 divide the sum by 19, and the quotient is the number of cycles elapsed 

 from the birth of Christ, and the remainder is the cycle for the given 

 year, or the golden number ; and if nothing remain, 19 is the cycle. 



Cycle of Indiction, a revolution of 15 years, but has no depeudance on 

 the motions of the heavenly bodies. It was used by the Romans for in- 

 dicating the times of certain payments made by the subjects to the re- 

 public, established by Constantino,, A. D. 312. To find it, subtract 312 

 from the given year, and divide by 15. 



Julian period. From the multiplication of the Solar cycle of 28 years, 

 into the Lunar of 19, and Indiction of 15, arises the Julian period of 

 7980 years, in which time they all return again in the same order. The 

 Julian'period, commencing before all the known epochs, is, as it were, 

 a common receptacle of them all, and to which they may all be reduced 

 (see JEra.) To find it, add to any year of Christ, 4713, and it gives the 

 year of the Julian period ; or subtract for any time before Christ 



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