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, C and D two contiguous points of the same as given in columns 

 2d and 4th of Table 1st, C/ 

 and SB two parallels of lati- 

 tude passing through these 

 points,^ the place where the 

 observation was made in a ver- 

 tical plane whose intersection 

 with the earth's surface is K H, 

 cutting the foregoing parallels 

 in E and H, and the projection 

 of the meteor's path in F. Also 

 let P represent the north pole of 

 the earth, and P M, P ff, P G, 

 P E, P D and P K meridians. 

 Then will the angle at ^be the 

 observed azimuth of the meteor ; 

 and knowing also the latitudes 

 of E and E, and the latitude 

 and longitude of K, the spheri- 

 cal triangles PE K and. PHK 

 wUl give the longitudes of E and H. Now the surface C N D Jf 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 Dhj L 

 and I, those of H and E by L' and Z', and the arcs ND, G D and F Ghjd,x and y 

 we can readily, from the figure, obtain the equations 



(L — I) {V — I) 



, -jj-1 ^iid 2/ = - 



d X 



{L — l} — {E -I') 



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.^ Each result was then verified by computing from the 



' 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, 1869. 



