gg RESEARCHES CONCERNING THE PERIODICAL 



limits assigned by this author for the elliptic elements of some of these bodies, 

 considered as asteriods, has been published in the proceedings of this Society 

 for August 21st, 1840. An examination of Professor Erman's analysis having 

 led to the conclusion that his limits for these elements are too restricted, and 

 that more simple formulae might be obtained by adopting instead of the earth's 

 actual velocity, the vv^ell known Gaussian constant as the unit of linear velo- 

 cities, induced me to undertake the discussion afresh. In doing so, hovfever, 

 it is proper to remark, as must be obvious to every one, that the nature of the 

 subject is such as to deprive the discussion of that demonstrative character 

 w^hich distinguishes the results of astronomy proper. Such a circumstance, 

 hov^^ever, should not deter us from aiming at the greatest precision in our 

 knowledge of the geometrical relations of these small bodies, which the nature 

 of the case permits. 



The principal data which the theory of shooting stars derives from observa- 

 tion are their relative velocities and directions as seen by an eye in motion, and 

 the dates of remarkable showers, or brilliant meteoric displays. These data, 

 if furnished with precision, are sufficient for the completion of their theory, 

 considered as cosmical bodies. In the case of a newly discovered planet or 

 comet, a single observation furnishes only a geocentric position, the distance, 

 relative velocity, and direction of motion, being as yet unknown. Hence 

 three successive positions, at known intervals, are required in order to deter- 

 mine, by Kepler's and Newton's laws, the (geocentric or heliocentric) distance, 

 velocity and direction of motion, at one of the three dates, — from which all the 

 elements of the elliptic orbit of the planet or comet may be derived. When 

 we consider the precision of observation, and the length of elapsed time, which 

 are requisite for determining the path of a planet or comet, it will appear sur- 

 prising at first, that enough should ever be known concerning the geometrical 

 relations of a body, which appears for a moment and then vanishes for ever, to 

 enable us even to form a conjecture concerning its true motion in the heavens 

 for an indefinite period past and to come. There are, however, several impor- 

 tant advantages in the case of shooting stars which do not present themselves 

 in a single observation of a newly discovered planet or comet. The shooting 

 star or asteroid is necessarily within a few seconds of its node, and its helio- 

 centric radius vector differs from that of the spectator by a quantity so small 

 as to be safely neglected in computations for the approximate elements of its 

 orbit. A similar remark apphes to the heliocentric longitude of the observer 



