OF A METEORIC FIRE-BALL. 39 



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, woidd 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, tUl 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 smaU 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" 



325° 10" 39" 



329° 23' 56" 



Inclination to the Ecliptic 



66° 12' 11" 



61° 9' 41" 



66° 25' 52". 



Semi-axis major (in miles) 



2005.32 



2005.32 



2005.32 



Eccentricity 



2.99836 



2.98110 



2,99214 



Longitude of Perigee 



264° 56' 43" 



215° 31' 1" 



261° 2' 6" 



Perigeal distance (in miles) 



4001.32 



3913.94 



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(l — e^) \(2a — r)h , . ^ ^o(l — e^)k 



r = — ^^ , V = J,-^ '- — -and sm 6 =^ — ^^ ^— 



1 + e cos iv ^ a r r 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 a 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 



