J38 E5SAYS AND OBSERVATIONS 



The three laft examples are taken from Dr. 

 Keir^ aftronomical Leftures, Ledure 23d. 

 and the numbers agree very nearly with his. 



In the orbits of Mercury and Mars^ if the 

 excefs of the angle BCD above the angle A 

 be added to the angle ACD, the fum will be 

 nearly the anomaly of the excentric reckoned 

 from the aphelion. 



In orbits of fmall excentriclty, the angle 

 ACD is nearly the anomaly of the excentric j 

 therefore the following rule will give the 

 anomaly of the excentric very nearly. 



From the logarithmic tangent of half the 

 mean anomaly, fubtradl the difference of the 

 logarithms of the aphelion and perihelion 

 diftances ; the remainder is the logarithmic 

 tangent of an angle, which call B : to the 

 angle B, add half the mean anomaly ; the 

 fum will give very nearly the anomaly of the 

 excentric. 



EXAMPLE V. 



In the earth's orbit, the mean diftance is 

 to the excentricity as looooo to 1691. Sup- 

 pofe the mean anomaly from the aphelion 

 to be 30°, it is required to find the anomaly 

 of the excentric. 



The 



