On the Collision of two Comets. 347 



an angle of 132° 2' 27.2", and that these two planes are inclined to 

 each other at an angle of 18° 6' 10.6". 



It now remains to ascertain the point in which the line of inter- 

 section of the two planes is cut by each of the orbits respectively. 

 For this purpose we will take for the aphelion longitude of Encke's 

 comet 337° 21' 2.4'^, the value determined by Encke himself, with 

 great accuracy. The aphelion longitude of Biela's comet is not 

 known with so great a degree of precision. Olbers gives 292° 39', 

 Clausen 296° 38', Damoiseau 289° 56'. Great exactness is not 

 necessary in this element, which is subject to considerable perturba- 

 tions, particularly from the action of the planet Jupiter. We will 

 take then for the aphelion longitude 293° 4' 20", the mean of the 

 three values given above, and we shall then have, for the instant in 

 which the comets pass the common intersection of the planes of their 

 orbits, the true anomaly reckoned from the aphelion, 



44° 26' 55.2" for Encke's comet, 



87° 10' 31.2" for Biela's, 

 and according to known formulse, the distances from the sun's cen- 

 ter are 



1.59881 for Encke's comet, 



1.59868 for Biela's. 

 Thus, it appears that the distance of the two comets, at the instant 

 of their passing the common intersection of the planes of their orbits, 

 is only 0.00013 of the semi-diameter of the terrestrial orbit, or about 

 12350 miles. 



A slight change in the elements, which, especially those of Biela's 

 comet, are subject to great disturbances, may greatly diminish, and 

 even totally annihilate, this distance, in which case the collision of 

 the two comets would take place in the direction of the line of the 

 centers. 



It follov^rs from the preceding investigation, that the point of space 

 in which this collision might occur is determined by the following co- 

 ordinates, referred to the center of the sun. 



Heliocentric longitude, Z=21° 0' 50" 



Latitude north, 6 = 9° 49' 46" 



Distance, r=: 1.5087 



The distance of this point from the nearest point of the terrestrial 



orbit, is readily found to be equal to v^l+r- ~2rcos.b, or 0.6349 



of the semi-diameter of this orbit. Consequently, if at the moment 



of contact, the earth should be in the vicitiitv of this part of its orbit. 



