94 



" that the line joining the planet and vertex of the tone moved with 

 " an equable motion." 



This complex hypothefis Seth Ward fhewed* to bfe precifely the fame 

 with regard to the motion in the ellipfe, as an equable motion about 

 the higher focus. At the fame time he gave two methods of comput- 

 ing the true from the mean anomaly on this hypothefis. One of them 

 was furnifhed by Neil, who is celebrated as the firll that ever ex- 

 hibited a right hne equal to a curve. This rule of Neil's is the ele- 

 gant and fimple one now fo well known, viz. " As the Aphelion dif- 

 tance : Perhelion diflance : : tang, of half the mean anomaly : tang, of 

 half the true anomaly." Ward afterwards affames, in his Aftronomia 

 Geometrica, this as the law of a planet's motion, and ftates himfelf 

 indebted to Boulliald for the hints that led him to the difcovery. Boulliald 

 is one of thofe to whom he dedicates his Aftr. Geo. in that dedication 

 he fays, " magna certe illius laudis pars in teipfum redundabit, qtii 

 *' aftronomia philolaica me ad hanc rem excitafti, promovifti, atque motus 

 " a^qualitatcm ad axem Coni adeoque (uti in inquifitione noftra ex 

 " principiis tuis oftendimus) ad umbilicum alteram ellipfeos referendo ad- 

 " juvifti."t This appears furprizing, when it is confidered that the an- 

 cients conceived an equable motion, about a point within the circular 

 orbit, equally diftant from the centre as the earth was. The tranfition 

 from this to the upper focus of the ellipfe was obvious. Kepler himfelf 

 remarks it more than once ;■[ but did not attempt to'fliew its connexion with 

 the equable defcription of areas. Ward, which is ftill more remarkable, con- 

 fiders| himfelf as having folved the problem propofed by Kepler. How 

 could it efcape him that the problem he had folved was not the problem pro- 

 pofed by Kepler, unlefs it had been ftiewn that the equable motion about 

 the higher focus refulted from the equable defcription of areas ? 

 ■ The method of Ward muft however, always be confidered as an 

 elegant and ufeful, although not a near approximation, except when the 



orbit 



* Inquifitio in Aftr. Boull. 



f Epit. p. 673, 6S1. 

 t Praf. ad Aftr. Gcom, 



