OF A METEORIC FIRE-BALL. 
41 
In Table 2d, the only columns that require explanation as to the mode of their 
computation are the 8th and the last five. The 12th and 13th show the points on 
the surface of the earth where the planes of the meteor’s path cut the vertical 
planes in which the different observations were made; and inasmuch as, owing to 
the earth’s rotation, the intersections of the former planes with its surface were 
not great circles, a rigid formula for computing these points would be quite com 
plicated, I adopted, instead, the following method, which, though not scientifically 
accurate, was made practically so within the limit of 1". 
Let A B represent the projection of a section of the meteor’s path upon the 
earth’s surface, G and D two contiguous points of the same as given in columns 
2d and 4th of Table 1st, G I v 
and S R two parallels of lati 
tude passing through these 
points, K the place where the 
observation was made in a ver 
tical plane whose intersection 
with the earth’s surface is K AT, 
cutting the foregoing parallels 
in E and H , and the projection 
of the meteor’s path in F. Also 
let Prepresent the north pole of 
the earth, and P ilf, P II, P G, 
P E, P D and P K meridians. 
Then will the angle at K be the 
observed azimuth of the meteor; 
and knowing also the latitudes 
of E and II, and the latitude 
and longitude of K, the spheri 
cal triangles P E K and. P H K 
will give the longitudes of E and K Now the surface G N D ilf being small, the 
curvature of the lines lying upon it may be disregarded, and the figure itself may 
be considered a trapezoid; and if we represent the longitudes of G and D by L 
and l, those of H and E by L' and 1', and the arcs N D, G D and F G by d, x and y 
we can readily, from the figure, obtain the equations 
d x 
and y — — 
x = _(L-l)(V- l) 
(.I —l) — (£' —I')' " L — l 
and by adding the values of y and x to the latitude and longitude of D , the lati 
tude and longitude of F for each observation, as given in the columns above men 
tioned, was obtained. 1 Each result was then verified by computing from the 
1 This is strictly true only of the first three series, extending down as far as No. 112. In the other 
two series, where less accuracy seemed necessary, the positions of F were determined, for the most 
part, by delineation and measurement on a large map, carefully drawn on a scale of about ten miles 
to an inch. 
6 April, 1809.