230 Royal Astronomical Society. 
anomaly a term proportional to the time, which does not exist in the 
absolute perturbations, and that it is, consequently, necessary to de- 
termine the value of and to subtract this term. This being pre- 
mised, w being the value of this term for a whole revolution of the 
comet; x the number of revolutions; A m the perturbations of the 
epoch of the mean anomaly; Az those of the longitude of the 
perihelion; A Q those of the longitude of the ascending node; A @ 
those of the angle of the eccentricity (e = sin); Ap those of the 
mean motion; i the inclination; we have 
(1—e)? 
dt=A y Cae Aw—2sin®> i AQ 
edhe. ViHe Waa ET Bata 
2 Ap! lee 
pe l—e 
« By substituting in these expressions the numerical values, which 
M. Encke has given at the place above quoted, we find for the pe- 
riod 
[) i — 
Of 1819, Jan. 27-25 to 1822, May 24-0ndt = — 6781-23 u=+4 9411 
, 1825, Sept. 163 =— 7930-22 =-+100-78 
1829, Jan. 9°72 = —124-42-—324 =-+ 5454 
“ For these four times we have the mean anomaly of Saturn, 
augmented for the sake of greater correctness by the great inequal- 
ity ; thus 
gi = 266" 8! 
= 306 42 
= 347 13 
= 27 44 
“ If we substitute these values, as well as the values of ¢, 0; 
3°322 ; 6°636; 9°952, in the preceding expressions of the absolute 
perturbations, we find for these four times, 
a“ “ 
not = —25'97 u = —66°38 
= —46°59 = +298:°94 
=— 812 = + 34°81 
pe = .— 12552 
«If we subtract from these the first-mentioned values, we obtain 
the perturbations for the three above-mentioned revolutions of the 
comet. Thus 
ndt = —20°62 u= + 95°32 
= +17:85 — +101°19 
= 422-40 = + 53°86 
«« By comparing these values of w with those given before as 
found by M. Encke, we obtain the following differences :— 
+ 1:21 
+ 0°41 
— 0°68 
« By comparing in the same way the values of n ét, we find im- 
mediately 
