126 RESEARCHES CONCERNING THE PERIODICAL 



in the same gulf, in 1838. Another opinion of Professor Olmsted, that the 

 radiant body was relatively at rest with respect to the observer, is at variance 

 with other known phenomena, since, according to the data of Section I., the 

 relative velocity of the separate asteroids in space was not much inferior to 

 that of the observer. Also, the radiant body itself, I suppose, must be given 

 up, as no such stationary position of a gravitating body is possible, a relative 

 motion being requisite to give sufficient centrifugal force to the body to pre- 

 vent it from falling at once to the earth. Moreover, it was remarked by 

 Professor Twining, and is now generally admitted, that the radiant and con- 

 vergent points are the perspective vanishing points of lines nearly parallel. 

 Professor Olmsted first adopted the half yearly period ^^ of a single cluster, to 

 explain the anniversary phenomena of 1799, 1832, and 1833. This he after- 

 wards relinquishes for a yearly ^^ period. I have shown that neither the half 

 yearly nor yearly period, with single cluster, will correspond well with the 

 table of relative velocities, nor with that of the serpentine meteor as determined 

 by Professor Twining. In reviewing Professor Olmsted's hypothesis respect- 

 ing the observer's and radiant body's equal velocities and parallel directions, 

 Mr. Espy^^ intimates that such a coincidence is not possible in a perihelion or 

 aphelion, but is possible in some part of the orbit of such a body. The follow- 

 ing view of this question, differing from both, is derived from the analytical 

 expressions for the tangential directions and velocities of any two bodies moving 

 in orbits round the sun : — 



'_2. j_\ _ p 



r sin u 

 (1) 



P 





In which 



a = asteroids semiaxis major, 



^ =s " linear tangential velocity, 



r = " radius vector, 



M = " angle between radius vector and tangent to orbit, 



y — " semiparameter. 



83 Sill., vol. xxix., p. 378. ^^ Idem., vol. xxxi., p. 393. 



s* Journal of the Franklin Institute, vol. xv., p. 10, note. 



