93 OUTLINES OF NATURAL PHILOSOPHY. 



far from the truth, in elliptical orbits of small 

 eccentricity. This solution was first proposed by 

 BULLIALDUS, a French astronomer, and was after- 

 wards adopted and improved by Dr SETH WARD, 

 and is known in this country by the name of 

 WARD'S Hypothesis. Another solution is distin- 

 guished, for the simplicity of the principles, and 

 the elementary nature of the reasoning employed, 

 viz. that given by the late Dr MATHEW STEWART, 

 in the Edinburgh Physical and Literary Essays^ 

 vol. u. (1755) p. 105. ; and again republished in his 

 Physical and Mathematical Tracts,}*. 4-04. Among 

 the other solutions, those of NEWTON, Prin. Math. 

 lib. i. prop. 30. Schol.; of SIMPSON, Essays, 4to, 

 (1740) p. 47. ; of EULER, Comment. Petrop. torn, 

 vu. ; and of IVORY, Edinburgh Transactions) vol. 

 v., (the latter extending to the most difficult case 

 of the problem, when the eccentricity is great), are 

 particularly commendable. 



Of all these, however, it may be said, that though 

 excellent when a numerical calculation only is re- 

 quired, yet when the solution is to be a step in the 

 investigation of other properties of the elliptic mo- 

 tion, they cease to be of use, so that recourse must 

 be had to such general theorems, as express the 

 true anomaly in terms of the eccentricity, and of 

 the mean anomaly. The first solution of this kind 

 was given by CLAIRAULT, Theorie de la Lune % 

 31. lemma 3d, &c. It was afterwards improved 

 and extended by other mathematicians, particular- 



