l8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 66 



orbit; let w be the true anomaly for the radius vector r, we then 

 obtain these quantities from the following equations : 



sini sinT=sin)8, 1 



cos isin T= — cos^- sin(0 — A), V (24) 



cos T= — cos ^ • cos( O — A), J 



(25) 



On account of the determination of the remaining elements, we 

 may refer to the computations of orbits and planets since all necessary 

 data have now been given. The quantities i and t must always Ijc 

 counted in opposite directions. If we count t from the prolongation 

 of the radius vector r toward the point 180° + O toward the sun, but 

 always in the first or second quadrant, then sin i always has the sign 

 of sin p. For the northern radiant, therefore, the corresponding'node 

 is always the descending node, hence we have ^ = O . Under this 

 assumption (viz. : positive jS) , the movement is toward either the right 

 Of left according as i lies in the first or second quadrant. For radiants 

 in the southern latitudes we have Q = i8o+ Q and the motion is 

 either toward the right or left according as i results from these equa- 

 tions in the third or fourth quadrant. In the subsequent presentation 

 of the elements, however, i will be given for the corresponding ascend- 

 ing node with the added words right or left motion, viz. : positive 

 or negative, direct or retrograde. Since for a considerable number 

 of the largest meteors (also so-called detonating meteors and even 

 also those associated with the fall of masses), it has been established 

 by the careful use of observations that the heliocentric velocity v for 

 the above-indicated parabolic limits is considerably exceeded so that a 

 may be negative and e greater than one, hence the heliocentric orbit 

 will be a well-marked hyperbola which on account of its position can- 

 not possibly have originated in the solar system, therefore it must be 

 assumed that such bodies have entered the solar system from the 

 outside cosmic space. 



Bodies that describe in space nearly parallel orbits at great distances 

 from each other with identical velocities belong therefore to a 

 sidereal stream of considerable extent, and can -intersect the earth's 

 orbit in such different nodal lines that excepting a which depends 



