130 RESEARCHES CONCERNING THE PERIODICAL 



These limits are derived from tlie principles of the geometry of position, and 

 have no reference to the limits of g and y, deduced from the laws of elliptic 

 motion. The most general interpretation of the cosmical theory of these as- 

 teroids is to suppose them to be moving in conic sections, in which those of 



(11) are the only necessary limits. In fact, the sporadic meteors, and the 

 clusters which have no known periodical character, may have for their orbits 

 either of the three conic sections. The case is quite different for the meteors 

 which appear at anniversary periods, and annually exhibit the same normal 

 velocity, too great to be ascribed to the errors of observation, and too uniform 

 at each appearance not to be the result of identity of elements. The first princi- 

 ple of inductive reasoning which leads us not to assign two causes for an event 

 where one is sufficient, would also lead us not to require for a series of con- 

 nected events the repeated exertion of a cause, where a primitive exertion of 

 it, and the subsequent action of known laws, are sufficient to account for the 

 succession. 



Now if we suppose that groups of bodies which, at yearly intervals, present 

 the same combination of elliptic elements, are moving in non-periodical curves, 

 (the parabolas or hyperbolas,) we must suppose that the primitive cause, what- 

 ever it may be, which gave to the bodies of our system their original projectile 

 motion is continually exerted afresh so as annually to present the appearance 

 just described. This is quite unreasonable; and accordingly, while we admit 

 that the three classes of conic sections are possible for the sporadic meteors, and 

 isolated clusters of unknown period, we must restrict those of anniversary oc- 

 currence to the class of ellipses, or periodical orbits, unless the observed rela- 

 tive velocity in Table I., combined with the convergent points in Tables II. 

 and III., should require the contrary. Now, in equation (i) the maximum 



2 2 



value of g'^ in a periodical orbit is {a being less than + cso ) equal to _ or — , 



r R 



neglecting the small discrepancies, or computing R for the position of the ob- 

 server, or meteor, if its distance from the observer is known. Then we have 

 for the maximum value of j^ in a periodical orbit 



(12) y = — G COS 4' + V \p — G^ sin* i^) 



The values of y in Table VI., computed from this formulae, are, when mul- 

 tiplied by X, to convert them into geographical miles per second, respectively 

 39.8 for the November meteors, 33.3 for those of August, and 12.0 miles for 

 those of December. As these values for August and November exceed the 



