APPENDIX. 63 



thefe, Mr STEWART lays down the doctrine of centripetal 

 forces, in a feries of propofitions, demonftrated (if we admit 

 the quadrature of curves) with the utmoft rigour, and re- 

 quiring no previous knowledge of the Mathematics, except the 

 elements of plain Geometry, and of Conic Sections. The good 

 order of thefe proportions, added to the clearnefs and fimpli- 

 city of the demonflrations, renders this Tract the beft elementa- 

 ry treatife of Phyfical Aftronomy that is any where to be 

 found. 



IN the three remaining Traces, our Author had it in view to 

 determine, by the fame rigorous method, the effect of thofe 

 forces which difturb the motions of a fecondary planet. From 

 this he propofed to deduce, not only a theory of the moon, but 

 a determination of the fun's diftance from the earth. The for- 

 mer is well known to be the moft difficult fubject to which Ma- 

 thematics have been applied. Though begun by Sir ISAAC 

 NEWTON, and explained, as to its principles, with fingular fuc- 

 cefs ; yet, as to the full detail and particular explanation of each 

 irregularity, it was left by that great Philofopher, lefs perfect than 

 any other of his refearches. Succeeding Mathematicians had been 

 employed about the fame fubject ; the problem of the Three bodies 

 had been propofed in all its generality, and in as far as regards 

 the motion of the moon, had been refolved by a direct and ac- 

 curate approximation. But the intricacy and length of thefe 

 calculations rendered them intelligible only to thofe, who were 

 well verfed in the higher parts of the Mathematics. This was 

 what Dr STEWART propofed to remedy, by giving a theory of 

 the moon that might depend, if poffible, on Elementary Geo- 

 metry alone, or which mould, at leaft, be the fimpleft that the 

 nature of things would allow. The Tracts were deftined to 

 ferve as the bafis of this investigation. We are not, however, 

 to imagine, that Dr STEWART intended to proceed in the fame 

 direct manner that CLAIRAULT, and fome other Geometers, 

 had done. It is not probable, that he believed this to be with- 

 in 



