40 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 G, CD, &c., the arcs of the same spoken above, and P the 



north pole of the earth — the arcs A P and 

 p G P, being the co-declinations of the points 



A and G were known, and also the angle 

 AP G, being their difference of right ascen- 

 sion. Hence the angle P A Goi the spheri- 

 cal triangle APG was readily found, which 

 in connection with the known sides A P 

 and ABoi 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 C and the side P C were 

 found; — and so on through each successive 

 triangle APD^APE, &c. The sides PB, 

 P C, &c., are the co-declinations of the meteor at the points B, G, Sec, 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.^ 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). 



' Ovei- a part of the visible track it was found more conyenient to reverse the process, and com- 

 pute the anomaly (column 14tb) and right ascension, for given differences of declination in column 2d. 



