114 



then fine «= and the firft approximated excentric anomaly=fl^io 



This method may be rendered much more convenient for praftice in the 

 following manner. 

 The cubic equation to be folved is 

 ^ 6. I — e 6m 

 s -i s = 



n — I .rri n. n — i e+i 

 This equation is readily folved by logarithms (fee page 57 of Dr. Maf- 

 kelynes excellent and ufeful introduction to Taylor's logarithms,) and the 

 following praftical rule deduced. 



Compute log. n(z='/5+>/g+i6) which call A 



3^/«^ — 1 e+i 

 the log. of which call B 



57, 296 n . r^ I 



8 . I — e which call C 



the log, of ^ 



«^ — I e+i 

 Thefe logarithms are conflant for a given orbit and the computation of 

 them will be facilitated by obferving that ^=^5+4 sec^ a being an arc 



the cotangent of which is ^^^ and ^^n^ — 1 ^+i=fec. b, b being an arc the 



tangent of which is s/n'' — i . e. 



Then m being the degrees in the mean anomaly. 



log. z,!^— ^z+20 

 Log. ;h +B+ 1 o=log. /, z =log. /, a. 



3 

 log J (fme^)=CM-Iog. ct. iu 



log. approximated excentric anomaly =log. a+A. Four places of loga- 



rithms will be fufEcicnt and the arcs may be taken out to the neareft minute. 



On 



