121 

 PRACTICAL RULE 



FOR 



OBTAINING THE TRUE FROM THE MEAN ANOMALY, 



I. Sublraa the Log. of the aphelion fromthe Log. of the perihelioti dif- 

 lance, and call the remainder B. B + the Log. tang, of ^ the mean 

 anomaly — the Log. tang, of an arch, which being added to ^ the mean 

 anomaly, the fum will be the approximate excentric anomaly. 



2. Jdd together the conjiant Log. 5.3144251, the Log. of the excen- 

 tricity and the Log. fine of the computed approximate excentric anomaly : 

 the fum diminifhed by lo -will be the Log. of a number of feconds to be 

 added to the approximate excentric anomaly, to obtain the correfponding 

 mean anomaly. 



3. Find the logarithm C either by a table previoufiy confiruded, or by 

 computation, viz. C — 19.6989700- 2 Log. cs ^ ^, '^ being an arch 

 the Log. cofine of which — Log. excent + Log. cs of the approximated ex- 

 centric anomaly. When the approximated excentric anomaly is greater than 

 90' ■» is alfo greater than go°. 



3. Jdd the log. of the error of the computed mean anomaly to C, and 

 the fum will be the logarithm of the error of the firtl approximated ex- 

 centric anomaly. This error has always the fame fign as the error of the 

 computed mean anomaly. 



5. The fum 0/ 5 B ayid Log. tang- i the corred excentric anomaly is 

 the Log. tang, of i the true anomaly. 



Note, when the mean anomaly is greater than 180'. Take its fup- 

 plement to 360, and compute the correfponding true anomaly : its fup- 

 plement to 360 will be the true anomaly required. 



Vol. IX. ( Q. ) ^y 



