14 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 66 



E. ZENITHAL ATTRACTION 



The velocity and the radiant point must for f urthef planetary com- 

 putation be corrected for the influence of the earth's attraction which 

 first increases and afterwards diminishes the approach to the zenith. 



If s is the zenith distance of the estimated apparent radiant at the 

 terminal point Lc, <i>c and 1/ the relative or geocentric velocity cor- 

 rected for the attraction of the earth and z' the zenith distance cor- 

 rected in the same way, then will ' 



where g is the acceleration due to gravity and 



20^7? =125 ..18, 



tan -^ = ^^- — , tan — 

 2 ^ + v 2 



(18) 



where all quantities are expressed in kilometers. 



The azimuth of the radiant suffers no change on account of zenithal 

 attraction. The equatorial co-ordinates of the radiant are, however, 

 to be newly computed with the help of this azimuth and the corrected 

 zenith distance. When these are used in the following text for the 

 computation of the planetary orbit, they will be designated by a' and d'. 



2. The Observations of Different Meteors Belonging to the 

 Same Stream from One Single Location on the Earth 



When many apparent paths belonging to the same radiant are at 

 hand which have been observed at only one place and within an 

 interval that is not too long, and when the changes in the co-ordinates 

 of the radiant during this interval are unimportant,'' or have been 

 taken into consideration, then these co-ordinates can also again be 

 determined according to the fundamental theorem that the paths 

 represent the most probable intersections of the respective great 



^ Schiaparelli, page 251. 



* The zenith attraction causes a larger or smaller appreciable change in the 

 location of the radiant together with the change in the zenith distance. This 

 may be quite notable in the case of meteors that strike the earth with small 

 velocity. Therefore we should combine into one determination only such 

 observations as those that are not too far apart with respect to zenith distance 

 of the radiant. In general, however, the dislocation in the position of the path 

 increases with the solar longitude, but remains for several days together within 

 the limits that have been indicated by the error of dbservation. The culmina- 

 tion of observations that cover a period of several weeks can in general only 

 furnish approximate results. [Note. — Such results are of absolutely no 

 value. C. P. Olivier.] 



