124 Prof. Encke on Olbers's Method of 



- * 7 r « dt + ™\r> Q r'Adt) + r' 4 d* 2 J T 



x#*-K 



— -" 1 



w« - -*^-i 



t" 3 , t" 4 d i» 



r 4 dt 



„__ , T 3 ! T* dV 



the expressions for the cordinates of the first and third places 



become 



.. dx' 



x — w t x — w„ -jj 



. dy 



x n = w' x' + w" -jj 



y= w/ y + w" -?j 



accurate to the fourth power of the times inclusively. Substi- 

 tuting these values in the above symbolic expressions [rr 1 ], 

 [r r"], [r 1 r"], for the quantities y' x — x' y 9 y" x — x n y, 



y" x — x"y', and remembering that x' -~- — y' -j— is the 



double areal velocity, consequently, according to Kepler's law 

 = Vp, p being the semi-parameter of the orbit, we obtain 



r n / f'» x t ,,s W* dr' \ 



or as only the ratios of every two areas are required 



[r'r"] r_f 1 _ y t 2 -t'* ^jV 3 dV \ 



[rr] ~t'\ L * H + * r' 4 ' dt J 



[r'i J '] m t L * r' 3 + * r'* " ' dt ' " J 



