VI. 



Some Methods of Computing the Ratio of the Distances of a Comet 



from the Earth. 



Br GEORGE P. BOND, 



ASSISTANT AT THE CAMBRIDGE OBSERVATOKV. 



{Communicated to the Academy, Jlpril 4, 184S.) 



The object of the following communication is to present some 

 methods of computing the ratio of the distances of a comet from 

 the earth from three observed positions, separated by short inter- 

 vals of time, in which, if required, the computations may be made (i) 

 directly from right ascensions and declinations. 



If necessary, any unfavorable influence from the direction, rela- 

 atively to the sun, of the comet's apparent motion may be avoided, 

 and account may be taken of parallax at the outset of the cal- 

 culations. 



The frequent references made to Dr. Bovvditch's Appendix to 

 his translation of the Mecanique Celeste are denoted by the letter 

 B. prefixed ; thus, B. [5994] (357) refers to the equation so num- 

 bered on p. 821 of the Appendix. 



I. If we denote by [rr], [?"' ''''], and [rr'l double the areas of 

 the triangles included between the three distances r, r', and r" of 

 the comet from the sun at the first, second, and third observations, 

 and the chords joining their extremities, and by z, 2!, and z" its 

 elevations above any fixed plane passing through the sun, we have 



13 



