68 ECCENTRIC ANOMALY. 



anfwersto 27" 41' 41', to which add half the mean anomaly, and the 



film - - 57 41 41 Will be the angle ACP, which in this example will 

 hi about 3" too imall, becaufe the right line ST, drawn at right angles to 

 PC continued if neceilrtry, and which is neaily the p;irt to be deduced from 

 the mean anomaly, will be fliorter than the arc PN. — Then to find the 

 value of ST: — fuppofe CA, or CP, to be equal to i or unity, then from 

 the elements of ft, SC will be equal to .04758735 and CP the radius 

 being equ.il to an arc of 57".29578, — SC will be equal to 2°, 7266, — then 



i6'.2ooo. This arc of 2" 1 8' 1 6" being dedu&d from 

 the mean anomaly will leave ^y" 41' 44'' for the eccentric ano- 

 maly correfted, and will be true within the -\ part of a fmgle 

 fecond. If a greater degree of accin-acy fliould be requifite, the 

 corrected angle 57" 41' 44" which fuppofe to be AGO, muft be 

 ufed to obtain the value of SR, and that value applied as above. 

 This correftion will only be ueceffary in cafes where the orbits 

 are very eccentric. 



But as the planets do not revolve in circular, but elliptical 

 orbits, the point O, in the arc AN, muft be reduced to r the 

 place of the planet in the curve of the ellipfe ; which is the point 

 cut by the right line OF drawn at right angles to AD. — The 

 angle AS r will then be the co-equate, or true anomaly ; and 

 may be had by the following analogy. — From the log. tang', of 

 half the eccentric anomaly, take the difference of the logs, of the 

 aphelion and perihelion diilances, and the remainder will be 

 the log. tang', of an angle ; to this angle add half the eccentric 

 anomaly, and call the fum U. Then to the log tang', of U, 

 add half the fum of the logs, of the aphelion and perihelion dif- 

 tances ; from that fum deduft the log. of the mean diftance, 

 and the remainder will be the log. tang', of the co-equate, or 

 true anomaly. — For example 



Frcm half the eccentric anomaly 28° 50' 52" log. tang. 9.7410263 



Dedu(S the diflF. of the logs, of the aphelionand perihelion diftances 0.0413649 

 The remainder 9.6996614 will be log. tang', of 26" 36' 5' 

 .'Vdd 4- the eccentric anomaly • 28 50 52 



CallthefumU - - • 55 26 57 



Then 



