116 



RESEARCHES CONCERNING THE PERIODICAL 



convergent point, namely, the antipode of the observer's true direction, is so 

 great that its connexion therewith does not appear, and the meteor is pro- 

 nounced to be unconformahle, non-convergent, or sporadic. 



Again, if the third and fourth laws are supposed to prevail, the earth must, 

 besides encountering the usual number of inferior and superior asteroids, also, 

 on certain occasions, traverse the planes abounding in flocks or clusters already 

 described, at the time when these clusters are in the nodes of their orbit. Still 

 these flocks or groups of asteroids are not necessarily seen, since they only 

 become visible to us when, besides being near their nodes, and we in the plane 

 of their orbit, their radius vector is also within a few hundred miles, or, rela- 

 tively to the earth's mean distance, sensibly the same as that of the observer. 

 The coincidence in point of time of these three separate events, with reference 

 to any one group or cluster of asteroids of moderate extent, supposing these 

 groups to be distributed either indiscriminately in the system, or, according to 

 a similar law to that which prevails relative to isolated asteroids, is a compound 

 event of extreme improbability. Indeed, the visibility of a portion of such a 

 group is only so far more probable than that of any isolated asteroid, as the 

 cubical contents of the group are greater than those of the earth. *^' Still, if the 

 number of groups is indefinitely great, the event must sometimes occur. And 

 if we attribute to our meeting with such isolated clusters the remarkable show- 

 ers in Quetelet's catalogue, the only elements wanting would be the dimensions 

 of these clusters, and an estimate of the annual number of isolated meteors en- 

 countered by the earth, in order to estimate the frequency of the distribution 

 of these clusters in the system, compared with that of the single asteroids. 

 When this complex event actually occurs, (our falling in with such a cluster, 

 the individuals of which have similar, though not perfectly identical elements 

 of motion round the sun,) the mean velocity of the group, in a plane normal to 

 the direction of the observer's motion, deflects the convergent point from the 

 antipode of the observer's direction. On such an evening, therefore, there 

 should be two convergent points, the one for the asteroids of the cluster proper, 

 the other the same as on ordinary nights. The convergent point for the clus- 

 ter having hitherto been regarded as the principal convergent point, the other, 

 if there be any, has always been overlooked, and all the isolated asteroids have 

 been termed unconformdbU or sporadic. 



•^3 This is not quite exact, but near enough in general terms. 



