1 22 



By the above operations, the true anomaly will be had to lefs than 

 a fecond, for ail the planets. In orbits more excentric, it may be 

 neceflary to repeat the fecond, third and fourth rules, ufing the cor- 

 refted excentric anomaly inftead of that firfl computed." And then ufing 

 the fecond correfted excentric anomaly to obtain a third, and fo on 

 till no error remains. The fuccellive correfted excentric anomalies will 

 rapidly approximate to the true excentric anomaly, as has been before, 

 ihewn. 



Although a fecond operation will never be neceflary for the pla- 

 nets, yet as a fecond operation is very readily performed, it may 

 be ufed for two rcafons. i. It ferves as a check, to verify the 

 correfted excentric anomaly, and 2. when the fine of the correfted ex- 

 centric anomaly is taken out from the logarithmic tables, the cofine of 

 the fame may be taken out, which will readily give us the logarithm 

 of the planet's diftance from the fun, viz. 2 Log. a, ^ <» - 19.698700 

 " being the arch, the Log. cs of which = Log. excentricity + Log. cs 

 correfted excentric anomaly. 



By 



