10 ON THE ORBIT AND PHENOMENA 
above, that the chords of small arcs of the orbit were sensibly equal to the arcs 
themselves, and that the time of describing each arc was equal to the quotient 
resulting from dividing the length of the chord by the mean of the velocities at its 
two extremities. So slight was the curvature of the orbit, even at its maximum, 
that the error in linear distance, resulting from the foregoing assumption, was less 
than of an inch in any one arc, or less than four inches in the aggregate of 
. these arcs for the whole visible track of 1300 miles. And the error in time was 
still more inconsiderable, being less than seven millionths of a second for the whole 
distance. The quantities in column 6th were obtained by adding these arcs suc 
cessively together, commencing at the point where the meteor first became visible. 
Those in column 7th were obtained by adding in like manner the linear values of 
the arcs, and those in column 8th, by adding in the same way the times occupied 
in describing them. The absolute time when the meteor passed the meridian of 
Washington, was estimated approximately, from direct observations of the time at 
several places, at 9h. 35m. to 9h. 37m; and, after several trials between these 
limits, to see what time would best satisfy the observations in which the position 
of the meteor was referred to the heavenly bodies, the time 9h. 35m. 32s. was 
finally adopted. By applying to this the quantities given in column 8th those in 
column 9 th were obtained. 
In the following diagram, in which A and G represent two known points in the 
meteor’s orbit, A B, B C, G Z>, &c., the arcs of the same spoken above, and P the 
north pole of the earth—the arcs A P and 
G P, being the co-declinations of the points 
A and G were known, and also the angle 
A P G, being their difference of right ascen 
sion. Hence the angle PAG of the spheri 
cal triangle APG was readily found, which 
in connection with the known sides A P 
and A B of the triangle APB , made known 
the angles at P and B , and the side P B. 
In like manner, in the triangle A P C, the 
angles at P and G and the side P G were 
found;—and so on through each successive 
triangle A P D, A P E, &c. The sides PB , 
P C, &c., are the co-declinations of the meteor at the points B, C, &c., from which 
the declinations or terrestrial latitudes in column 2d were obtained. The angles 
at P measure differences of right ascension, which added severally to the right 
ascension of the point A, gave the quantities in column 3d. 1 The angles at B , G , 
&c., show the true course of the meteor at these points (column 10th), and having 
its velocity given in column 14th, and knowing also that of the earth’s rotation 
directly beneath it—viz., the velocity at the equator multiplied by the cosine of 
the latitude—it was easy to compute the apparent course (column 11th). 
1 Over a part of the visible track it was found more convenient to reverse the process, and com 
pute the anomaly (column 14th) and right ascension, for given differences of declination in column 2d.