OF A METEORIC FIRE-BALL. 
39 
t 
viz., that in section 3d the retrograde motion of the perigee increased up to a certain 
limit, and then diminished, is easily explained, when we consider that at the com 
mencement of the section, near the perigee, the motion of the meteor was nearly 
horizontal, so that there was but little change in the density of the air through 
which it passed. If the density were uniform, the retrograde motion, commencing 
with zero at the perigee, would have continued to increase; but as the meteor con 
tinued to rise higher above the surface of the earth, the diminished density of the 
atmosphere at length neutralized this increase; after which the motion became 
slower and slower, till at the height of near 64 miles it became wholly unappreci- 
able. In the determination of quantities so minute, more accurate tables are needed 
than any which were accessible, and could such have been obtained, the results 
would doubtless have exhibited more conformity to law. In those employed, the 
decimals were carried to only seven places, which were extended, in the calcula 
tions, two places farther by proportional parts. 
As the body of the meteor continued to throw off fragments in the lower portion 
of its path, it is not improbable that there were other slight changes in the elements 
beside the two already mentioned. Indeed, the observations would be better satis 
fied by supposing a very slight one to have occurred in the horizontal elements (viz., 
the inclination of the orbit and the longitude of its nodes), not far from the meri 
dian of Nantucket; but if it truly occurred, it was so small as to be hardly worth 
noticing. At each rupture there was doubtless a change in the velocity, and con 
sequently in the length of the major axis, but there were no satisfactory data for 
determining the amount, and it too was disregarded. 
• The elements of the three sections, as finally adopted, were as follows:— 
1st Section. 2d Section. 
3d Section. 
Longitude of Descending Node 332° 56' 14" 
Inclination to the Ecliptic 66° 12' 11" 
Semi-axis major (in miles) 2005.32 
Eccentricity . . . 2.99836 
Longitude of Perigee . 264° 56' 43" 
Perigeal distance (in miles) 4001.32 
325° 10" 39" 
61° 9' 41" 
2005.32 
2.98110 
215° 31' 1" 
3913.94 
329° 23' 56" 
66° 25' 52". 
2005.32 
2.99214 
261° 2' 6" 
3994.88 
and according to these elements, the meteor entered the sphere of the earth’s domi 
nant attraction from the direction of the constellation Sextans, near the left fore 
foot of Leo, Right Ascension 147° 41', Declination 3° 8' north ; and left toward 
a point in Right Ascension 355° 2' 9", Declination 30° 56' 42" south. 
By means of equations already given, viz. :— 
a (1 —e 2 ) 
1 + e cos w 
v = 
and sin 6 
^ ct( 1 —e 2 )7i 
T V 
the values of r —3956,?; and the complement of 6 (Table 1st, columns 5, 14 and 
12) were computed for the different values of o assumed in column 13th. 
The linear values of the several arcs intercepted between the points thus indi 
cated, and the time occupied in describing each, were next required, but instead 
of computing them from the customary differential equations of space and time, I 
employed the easier, though less scientific, method based on the assumption, as