34 ON THE ORBIT AND PHENOMENA 
ning anew, and would gladly leave the work to other hands, for a more critical 
investigation. 
In prosecuting the investigation, the method of procedure was as follows: The 
first effort was to obtain approximately the parallax and position of the meteor at 
different points along its path, by means of pairs of observations taken on or near 
the same vertical circle. And not suspecting any change in the elements of the 
path, but supposing it to be one and the same curve throughout, I endeavored from 
about a dozen such pairs, which the series of observations furnished, to select three 
that seemed most reliable, in order that, by means of a polar equation of the orbit 
for each of the three points determined by them, I might find the major axis, eccen 
tricity, and true anomaly, and consequently the longitude of the perigee. As the 
orbit, if undisturbed, must necessarily be in the plane of a great circle about the 
earth, either of the two points thus found would, moreover, determine the inclina 
tion of the orbit, and the longitude of the node. Could these equations have been 
obtained, they would have read 
r _ a 0 -—*?) / = a C 1 — e ') and = «o —<0 
1 -he cos 6) 1 + e cos ( a + 6) 1 + e cos (cj + S') 
in which r, r' and r" represent the radii vectores at the three different points, a the 
semi-axis major, e the eccentricity expressed in decimals of the semi-axis major, o 
the true anomaly at the point farthest east, and S and the differences between this 
anomaly and those of the other two points respectively, as determined by the obser 
vations. Unfortunately, however, there were but two pairs of observations that I felt 
could be relied upon sufficiently to use them for this purpose; but having what 
seemed to be a careful determination of the velocity of the meteor’s motion near 
the point indicated by one of them, I used, instead of the third equation, the follow 
ing, which expresses the relation between this velocity and the major axis of the 
orbit, viz: — 
h r 
a = o 
2 h — rv 
in which v represents the velocity, and h the force of gravity, at the unit of dis 
tance (one mile) = 32^ feet x (3956) 2 . 
Having thus obtained an approximate orbit, I proceeded to compare azimuths 
and altitudes deduced from it, with those given by the various observations, to see 
what modifications were required in the orbit, in order to satisfy them. And by 
repeated modifications in this way—over fifty in the aggregate—the results given 
in the tables at the end of this memoir were finally arrived at. The value of v as 
deduced from the foregoing equations, was 7 J miles per second, relative to the 
earth’s centre; but this was found to be too small, rendering the orbit too much 
curved, and after trying other values, ranging from 7f to 11 miles, the value 9f miles 
was finally adopted, as best satisfying the observations; thus showing that the orbit 
was hyperbolic. As thus modified, the first approximate orbit satisfied tolerably well 
most of the reliable observations west of about longitude 76° or 77°, near which 
the most easterly of the two points, from which the orbit was determined, was 
located; but further east the discrepancies were so great that they could be recon-