134 ESSAYS AND OBSERVATIONS 



is the log. of o'.0927774; the angle DCG 

 therefore is o'. 0927774; therefore the angle 

 ACG, the anomaly of the excentric, is 

 55'.oi24588. 



EXAMPLE III. 



. Supposing the mean anomaly in the fame 

 orbit to be 45°, it is required to find the ano- 

 maly of the excentric. 



The log, tang, of 22° 30' is 9.617224^ 



The difF. of the logs, of AS, SP is 0.0806085 



The difference 9.5366158 



is the log. tang, of 18° 59.1327325, half the 

 difference of the angles CSB, CBS j the 

 angle CSB, that is the angle ACD, therefore 

 is 41° 29'.i327325 ; and the angle CBS or 

 BCD is 3'>3o'.8672675. 



The log. tang, of half the angle 



ACD is - 9-57^3203 



The diff. of the logs, of AS, SP is 0.0806085 



The ^difference 9.49771 18 



is the log. tang, of 17' 2y'.jo%2.6j2y half 

 the difference of the angles CSD, CDS ; 

 the angle CDS or DCF, therefore, is 



3° i6'.858o99. 



