101 



Hence reducing thefe equations, 

 a=m+a-i-a+&!.c. 



=m — 2esm+i,2^6oye s, 2m+o,ygS27e s, ?«— 1,284075 j-, yn &c. 



2 -^ 3 



but true anom.=OT — zesm+\,2^e s, 2m-\-o,2^e s, ;«— 1,08333? j, 3m &c 



Therefore the error of Mercator's anomaly 

 = — 01393^ -fj 2'«+o,54837e s, m — 0,201375 s, 3;;; &c. 



The greateft error in the orbit of Mercury -will be 22'^ nearly, 

 and in the orbit of Mars 2' 7". Hence this hypothefis of Mercator gives 

 the place of a planet fomewhat lefs accurately than Boulliald's correc- 

 tion of Ward's hypothefis. 



The following Table fliews nearly the maxima of the errors of the 

 three hypothefes of Ward, Boulliald and Mercator, for all the planets. 



The mean anomalies, when the refpeftive errors of thefe hypothefes 

 are greateft, may be found fufficiently near as follows. The errors deduced 

 will in Mercury and Pallas, differ a few feconds from the truth. In 

 Seth Ward's hypothefis ff2=, 7854+ j_e + _I_£■^ In Boulliald's m = go° 



2\/2 3 

 and in Mercators, the cofine of -m = -,o"7. This laft expreflion evi- 



e 

 dently will not apply to the Earth and Venus. For them, ftriaiy, the 



folutiou of a cubic equation is neceflary, but the limit of the error is 

 otherwife obvious. 



On 



