229 On the Planet Festa. 



iiishing the force at the expense of the lime, or the velocity 

 at the expense of the force; or rather by employuig two or 

 more forces instead of one : this gives an infinity of resources 

 for producing the momentum of activity necessary: but, 

 whatever we do, these means must always be equal, i. e. 

 the momentum of activity consumed by the soliciling forces, 

 is equal to the effect or momentum exercised at the same 

 time by the resisting forces. 



[To be continued.] 



XLI. On the Planet Fes fa. Brf S. Guoombridge, Esq. 

 To Mr. Tilloch. 



SIR, 



X HE discovery of the planet Vesta, on the 29th of March 

 1807, having been communicated to this country by Dr.. 

 Olbers ; on the 26th of April I found its place, and observed 

 the same on the meridian. I obtained a series of observa- 

 tions to the 20th of Mav ; after which, from the increase of 

 daylight, it was no longer visible on the meridian. The 

 observations which were afterwards made were with equa- 

 torial instruments ; and these cannot be depended on, for 

 sufficient accuracy in calculating the elements. I have^ 

 however, used some of these, from the 29th of March to 

 the 22d of June, to determine the eccentricity ; those which 

 were made on the meridian producing nearly the same ra- 

 dius. I thence discovered, that the planet was decreasing 

 in radius, and therefore conjecture that it was in aphelio 

 about the time it was first seen. When the planet was dis- 

 covered by Dr. Olbers on the 29th of March, it appears to 

 have been about seven days past the opposition; and it ia 

 well known, not having that point of the orbit for a datum, 

 the difficulty of calculation is increased. 1 was therefore 

 anxious to observe the planet before the ensuing opposition,, 

 to obtain sufficient materials for ascertaining all the elements. 

 For this purpose, I assumed a mean radius of the extreme 

 observations; which, if I was right in my conjecture of the 

 aphelium, would prove too great; and therefore the planet 

 should be further advanced in the ecliptic. On the 30lh of 

 July, the evening being clear, and the moon not risen, I 

 obseived the difference of right ascension of several stars of 



the 



