174 A NEW METHOD OF DETERMINING THE GENERAL PERTURBATIONS, ETC. 
observation, p the radius of the Harth, and =z the equatorial horizontal parallax of the 
Sun. 
For the difference between computed and observed place we have 
O— 0 = — 2’ 37.7 in right ascension, and C’— 0 = — 57’7 in declination. 
- By the method just given we have found the positions of the planet for several 
dates and have compared with the observed places. The comparison shows outstand- 
ing differences too large to be accounted for by the effects of the perturbations yet to 
be determined, which are the perturbations of the second order, with respect to the 
mass, produced by Jupiter, and the perturbations produced by the other planets that 
have a sensible influence. We have therefore corrected the elements that have been 
used in the computations thus far made, by means of differential equations formed for 
this purpose, employing as the absolute terms in these equations the differences be- 
tween computation and observation for the several dates. A solution of the equations 
has given corrections to the elements that produce quite large effects on the computed 
place. Thus recomputing the position of the planet for the date given above with the 
corrected elements we find 
a, = 340° 33’ 44.5 , 6, = — 2° 2 15”6. 
And since 
oy = 840° 33’ 49”.1 , 6) = — 2° 2 25” 4 
we have, for the difference between computed and observed place, 
C— 0 = — 4’.6 in right ascension, and C— O = + 9’.8 in declination. 
