i68 Mr. Ivory on a new Method of deducing 
known elements of the orbit. Now the elements employed 
by Legendre in computing the places of the comet used in 
this example, are these, viz. 
log. of perihelion dist. 9 090847 
Time of passage, Oct. 7*53io; 
from which data I have calculated the radii vectores and the 
true anomalies for the 8^h and 12th of September at 14^ as 
follows, viz. 
September. 
Log. of Rad. Vect. 
Anomaly. 
d. h. 
8 14 
9-968361 
137 17 35 
12 14 
9.920961 
134 46 10 
Angle between r and r* 
2 31 25 
These quantities differ very little from the results obtained 
above : the errors are indeed hardly greater than the dis- 
crepancies which it is difficult to avoid in a complicated cal- 
culation, viz. first computing the geocentric longitudes and 
latitudes, and then going back from these to the elements of 
the orbit. 
The exactness of the approximation is sufficiently proved 
by the comparison already made : but I have likewise calcu- 
lated these two elements, viz. 
log. of perihelion dist. - 9*09 1920 
Time of passage, Oct. - 7*5403 
the perihelion distance being ^r^th part too much, and the 
time of passage about later than the true time. These 
errors, although very ijmall, are yet greater than might be 
