98 



I. s: 



2. s=5f'j, 2m z=e s, am 



2 4 



3- is =0 



4- z — 2.^e z=2^ •^'^^ or_s =— if j, 4« Jcc. 



2 1.4 32 



Therefore 2=;«+ Elf s, 2m — ^'^e s, 4m kc. 



and from thence s, z=s, m-^^e s, yn+s, m 

 s, 2Z—S, 2m+^e s, 2m 



■: s, 4Z=s, 4m 



But by the above theorem 



The < PSH=s — 2W, s+sf s, 22; — &c. 



I 2 



in which by fubftituting for z j,s &c. 



The < P S H or BouUiald's anomaly 



2 ^ 



— 7Ji — 2es, m+le s, 2ni — \s, m le -\-\s, am 7 "„ 



—'-t¥> 3'« 5 +i5'f> 4« 5 ^ '^• 



comparing this with the true anomaly, its corredion will be found to be 



{s, m le — tVj, 2m ? ^"^cc 

 — s-fj 3m 5 —^\s, 4m 5 * 



The maximum of this correflion in the orbit of Mercury, is nearly 

 20' ; in that of Mars nearly 2', a quantity fcarcely difcoverable by the 

 obfervations of Tycho Brahe. In the orbit of Jupiter the greatefl error is 

 nearly 16", in the earth o". So that this method of computing the anomaly, 

 was, in rcfpeft to the obfervations by which Boulliald examined his hy- 

 pothefis, fufficiently accurate for all the planets except Mercury. It 

 appears alfo, from what has been done, that the maximum of error, 



in 



