E Q U 



EQUATION of Time. 



The equation of time, relatively to its causes, depends on two circum- 

 stances; (1) the obliquity of the ecliptic j and (2) the unequal angular 

 motion of the s^n in its orbit. The equation of time, as arising- from 

 the first cause, wouldbe " (Tie^'difference of the sun's longitude and its 

 right ascension converted into time. In the first and third quadrants, 

 apparent time would precede true ; in the second and fourth quadrants, 

 true time would precede apparent j and at the Tropics and Equinoxes, 

 true and apparent time would coincide. Also upon this supposition, 

 the equation would be a maximum at 4 points, viz. when the cosine of 

 the sun's declination is a mean proportional between radius, and the 

 cosine of the obliquity of the ecliptic. 



The equation of time, as arising from the second cause, would be the 

 difference between the true and mean anomaly. Hence true and appa- 

 rent time would coincide at the higher and lower apsides. From the 

 higher to the lower apside, apparent time would precede true ; from the 

 lower to the higher apside, true time would precede apparent. The 

 equation, in this case, would be greater at two points than at any other, 

 viz. when the earth's distance from the sun is a mean proportional be- 

 tween the | axes of its orbit. To find it, when both causes are consider- 

 ed together, let A be the sun's time right ascension, M his mean longi- 

 tude, v the equation of the Equinoxes in longitude j then v X cos. 

 obliquity = the equation of the Equinoxes in right ascension, and 



Equation of time = A - M -, X cos, obliquity 

 15 



which is to be added to apparent time if positive, and subtracted if 

 negative. 



As the sun's true right ascension is deduced from the true longitude 

 and the apparent obliquity of the ecliptic, both of which vary from one 

 age to another ; hence tables of the equation of time, constructed for 

 any one time, are not true for another. The following Table, there- 

 fore, taken from the Nautical Almanack for 1828, or leap year, though 

 inapplicable when any very nice determinations of the time are requir, 

 d, may yet be xiseful for regulating common clocks or watches, as the 

 error for the next half century will only amount to a few seconds. 



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