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 



..= ^1=^ / ^:=f!) and/'=,_^=^) 



1 +e cos cj 1 + e cos(^g) + o) 1 + e cos (o + o ) 



in which 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 6' 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: — 



7ir 



a = :- 2 



2 /i — 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)1 



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| 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 7| to 11 miles, the value 9.| 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 Avhich the orbit was determined, was 

 located ; but further east the discrepancies were so great that they could be recon- 



