2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL.. 66 



mines the geocentric direction of the observed rectihnear portion of 

 the path. This is, however, except for the influence, of the attraction 

 of the earth, which can easily be allowed for, determined by the 

 resultant of the velocity of the earth reversed and the true helio- 

 centric velocity of the meteor. The projective direction of the latter 

 motion as seen on the sky is the true radiation point or radiant which 

 thus determines the true direction of the path of the meteor at the 

 node. 



Since the sun must lie in the plane of the orbit of the meteor this 

 plane is determined by the radius vector to the sun and the direction 

 of the orbit at its node, or by the great circle on the sphere that con- 

 tains the points representing the sun and the true radiant. 



But this latter also gives the angle that the true direction of the 

 path makes with the radius vector at the node and thus all further 

 elements of the orbit depend upon the velocity at this portion of the 

 orbit, which must be determined either from the observations or from 

 theoretical considerations. 



The problem now before us consists, therefore, of two very dififer- 

 ent portions sharply separated from each other, of which the first 

 is a geocentric problem, the second concerns the heliocentric con- 

 ditions. These portions are : 



1. The determination of the radiant point and of those quantities 

 which are necessary for estimating the relative velocity. 



2. The location of the orbit in the solar system. 



With reference to the first part which contains the more difficult 

 and complicated work, but whose results must be decisive as to the 

 further results of the second part, the starting point and the aim can 

 be dift'erent. The most important cases of the determination of the 

 radiant arc the following : 



1. Examination of the path relative to the earth and of the radiant 

 point by means of numerous observations of tlie same meteor from 

 different places on the earth's surface (corresponding observations 

 in the most general sense of the word). 



2. Determination of the radiant by observations of several apparent 

 paths belonging to the same radiant and seen from one station (one- 

 place observations). 



I. DETERMINATION OF THE RADIANT AND THE GEOCENTRIC 



VELOCITY 



I. Numerous Observations at Different Places 

 Abundant experiences teach vis that, depending upon the location 

 of the orbit with reference to each individual place of observation. 



