94 
lies and radius-vectors in duplicate, once by means of a man- 
uscript table to supply the reductions needed for N1coLar’s 
formulas, which proved more convenient than BARKER'S 
table for an orbit of so small a perihelion distance, and then 
again by means of the Besselian reduction of the parabola 
to an ellipse. 
New equations of condition were now formed, sixty-six 
in number, — weights were empirically assigned to each, 
and a fifth system of elements thus found which absolutely 
represented the Portland observation, and satisfied the two 
Chihuahua altitudes so admirably that the greatest discord- 
ance of the five amounted to but 37”, while the probable 
error of a normal place amounted to 16”. Separating the 
observations made with a ring-micrometer from those ob- 
tained by the filar micrometer, he was able to assign more 
accurate weights to the several measurements of each co- 
ordinate, and found, as might have been anticipated, that 
the probable error with the ring-micrometer did not much 
exceed that with the filar micrometer for differences of right 
ascension, while it proved to be nearly in the ratio of 7 to 
10 for differences of declination. 
By a repetition of the process, after assigning carefully 
computed weights, as above mentioned, to sixty-five normal 
equations of condition, Husgarp obtained by the method 
of least squares a sixth system of elements, which gave the 
best possible representation to the entire series of observa- 
tions, and reduced the probable error of a normal place to 
less than 13”, 
Here the investigation might well have rested; for the 
effect of terms of the second order, both in the perturba- 
tions and in the comparisons, might fairly be considered as 
removed, and the sums of the squares of the residuals were 
aminimum. But Hussparp was not content to leave any 
sees Scerel 
core 
