IQQ PROBtEMS IN SPHEROiDAL tRIANGLES. 



compared with that at the equator, gives yf^ for the com- 

 prefTion. W<i may therefore aflume •j'g-j- as being very nearly 

 its true value. 

 fromeeleflUlir- It is a curious circumftance to find the figure of the earth, 

 regularities j deduced from the meafurement of lines and angles on its fiir- 

 face, confirmed (perhaps correfted), by obfervations of the 

 fiars and planetary bodies in the heavens, combined with the 

 theory of univerfal gravitation. But fuch is certainly the cafe. 

 t.g, of the Among others may be mentioned two fmall inequalities in the 

 BQoon. moon's motion, which the induftry of modern mathematicians 



have unfolded. One of them was firll taken notice of by 

 Mayer, and fixed by Mafon at 7",7, but was neglefled by 

 aftronomers, as it did not fufficiently appear that fuch an equa- 

 tion Ihould arife from the theory, till Laplace traced it to the 

 ob'atenefs of the earth's figure. Its argument is the longitude 

 of the moon's node, and its value has been found by Burg, 

 from the obfervations of Dr. Maflcelynp, to b,^ equal to 6'',8, 

 which anfwers to a compreffion of y^y.^jy Thigre is alfo an- 

 other inequality of ti)e moon's motion in latitude, which de- 

 pends on the fine of the true longitude, and refults from a 

 nutation in the lunar orbit, produced by the ad^ion of the ter- 

 reftrial fpheroid. Burg has alfo determined the coefficient of ~ 

 this inequality, from a great number of obfervations, to be 

 equal to S'^O, which refults from a compreffioH of •j-ot.'S'* 

 Remarks upon The preceffion of the equinoxes, and the nutation of the 

 Newton's difco- ^,^j.j]^,^ | ^ difcovered by Newton to arife from the ob- 



very and invelh- , ' -' _ 



gation of this latenefs of the earth's figure. This famous problem is acknow- 

 lubJKdt. ledged to be one of the mod abftrufe in phyfical afijonomy, 



and its complete folution requires the utmoft refources of the 

 modern analyfis. The compreffion thence arifing is equal to 

 T*T' ag''cerng exa(5lly with the refults from the two lunar in- 

 equalities, the lengths of the fecond pendulum, and the befl 

 meafurements on the earth's furface. It is well known that 

 Newton failed in attempting to folve this problem, and fome 

 French mathematicians have been difpofed to pride themfelves 

 on being the firft todetedit. It ought however to be remem- 

 bered, for the honour of that great man, that his miftake did 

 nut arife from any error in principle, but from his taking for 

 granted, without demonltration, a circumfiance which ap- 

 pears highly probable, but is really erroneous. He feems to 



have 



