97 



the correaion to be applied to Seth Ward's anomaly appears to be 



The maximum of this correftion in the orbit of Mercury, amounts to 

 ^33 nearly. In the orbit of Mars to nearly '7;,, a quantity readily detefted 

 by the obfervations of Tycho Brahe; and hence this hypothefis was 

 juftly difregarded by Kepler. 



On Boulliald's correaion of Seth Ward's Hypothefis. 



Boulliald, difpleafed at the treatment he had received from Ward, 

 in return fhewed that the hypothefis of equable motion about the higher fo- 

 cus, would not give the places of Mars agreeably to obfervation, and 

 propofed the following conftruftion, for determining the place of a 

 planet. A conftruftion admitting of an eafy calculation. 



Make the angle A H R = mean anomaly (jn), H being the higher ^^g. 

 focus, draw D R Q^ parallel to the axis minor, and meeting the circle 

 in q, and draw Q^P H interfefting the orbit in B, which will be the place 



of the planet. 



To compare the anomaly fo determined with the true anomaly, the ' 

 value of P S H {a) is to be obtained in a faies afcending by the 

 powers of the excentricity. 



Let Q^H A = z, then 



tang, z : tang, m : -..i -. ^\—e or log. t, z=log. t, m—^ log. i- 

 from which equation, by taking the fuccefEve fluxions per Saltura, z will 



be obtained. When e-o ai;d z-m and e is conftant. \ 



Vol. IX. N ' «• 2= 



