APPENDIX. 69 



number and extension ; and whatever pretexts Moralifts or Di- Account of 



. . . Dr Stewart., 



vines may have for abufing one another, Mathematicians can 

 lay claim to no fuch indulgence. The afperity of Mr LAN- 

 DEN'S animadverfions muft not, therefore, pafs uncenfured, 

 though it be united with found reafoning and accurate difcuf- 

 fion. The error into which Dr STEWART had fallen, though 

 before taken notice of by Mr DAWSON, was firft exactly deter- 

 mined in the work before us *. But Mr LANDEN, in the zeal 

 of correction, brings many other charges againft Dr STEWART, 

 the greater part of which feem to have no good foundation. 

 Such are his objections to the fecond part of the inveftigation, 

 where Dr STEWART finds the relation between the difturbing 

 force of the fun, and the motion of the apfides of the lunar 

 orbit. For this part, inftead of being liable to objection, is de- 

 ferving of the greateft praife, fince it refolves, by Geometry 

 alone, a problem which had eluded the efforts of fome of the 

 ableft Mathematicians, even when they availed themfelves of 

 the utmoft refources of the integral calculus. Sir ISAAC NEW- 

 TON, though he aflumed the difturbing force very near the 

 truth, computed the motion of the apfides from thence only at 

 one half of what it amounts to in reality ; and fo, had he been 

 required, like Dr STEWART, to invert the problem, he would 

 have committed an error, not merely of a few thoufandth 

 parts, as the latter is alleged to have done, but would have 

 brought out a refult double of the truth f. MACHIN and 

 CALLENDRINI, when commenting on this part of the Prlici- 

 pia, found a like inconfiftency between their theory and obfer- 

 vation. Three other celebrated Mathematicians, CLAIRAULT, 

 D'ALEMBERT and EULER, feparately experienced the fame dif- 

 ficulties, 



* IT is but juftice to remark, that Mr LANDEN had probably never feen Mr DAWSON'S 

 Proportions at the time his own were published, the whole impreflion of them, almofr, 

 having been burnt by a fire which confumed the warehoufe where they were lodged. 



f Prin. Math. lib. 3. prop. 3. 



