VOL. LXXVII.] PHILOSOPHICAL TRANSACTIONS. 305 



TEM, then will st be the precession of the equinox during the time the sun 

 describes if in the ecliptic. Now Erf (or ec, as the angle at e is indefinitely small) 



: dc :: rad. = 1 ; sine angle e = — ^— ^; hence (if sv be drawn perpendicular to 



V . Saprvwy Saprvw x sln.SE X^ ,i r 



TE) 1 : sme se :: —^ — - : sv = —^ -; tnereiore, sm. stv or esp : 1 



/ p P 



Saprow X sin. SF. x_y 



:: sv : st = —^ : -. 



p X sm. ESP 



^^ t; - , COS. sp , vw sin. sp x cos. sp , 



8. Now -: = sm. SP, and w = , hence -: = ; but 



sin. ESP COS. Es' sin. fsp cos. es 



COS. ESP , 1 ^a-' sin. SP x cos. sp x cos. esp sin. 2sp' x cos. f.sp 



= 1, nence -.- — — 



tan. ES x cot. sp sin. esp cos, ks x tan. es x cot. sp sin. es 



^, 3flpr X sin. sp^ X cos. ESP xi /•/• • >. 3a»r x cos.esp x a;^;f 



consequently, st = -^ ^ = (if ar = sm. sp) ;^ v(i-x«) > 



^/ItlV y COS FSP X t/ 



whose fluent, when a; = 1, is —^ — ^ (y being now = to a quadrant) 



the arc of precession while the sun describes 90° of the ecliptic; and to find the 



1 . «^^o 3apr X COS. esp x V ^r^o v. ^^P^ X cos, esp . 



degrees say, 4y : 360 :: —^ — : 300 X -^ — — , consequently 



the precession in a year = 36o° X — — ^~— — = 2l" 6'". This would be the 

 precession of the equinox arising from the attraction of the sun, if the earth 

 were of a uniform density, and the ratio of the diameters as 229: 230; but if 

 the greatest nutation of the earth's axis be rightly ascertained, the precession is 

 only about 14-|-"; which difference between the theory and what is deduced from 

 observation, must arise either from the fluidity of the earth's surface, or an in- 

 crease of density towards the centre, or the ratio of the diameters being different 

 from what is here assumed, or probably from all the causes conjointly. But as 

 the best observations must be liable to some small degree of inaccuracy, and an 

 error of 1 or 2 seconds in the nutation will, in this case, make a very consider- 

 able alteration in the conclusion, the estimation of the precession arising from 

 the action of the sun seems to be subject to a very considerable degree of uncer- 

 tainty. 



VOL. XVI. 



Rr 



