420 Olbers' Essaj/ on Comets. 



of his failure, for the method is as little adapted to finding 

 the true distance, as that of Bouguer. If we suppose the 

 earth to describe a right line during the observations, with an 

 equable velocity, the problem will become indeterminate ; con- 

 sequently, the curvature of the earth's orbit must afford the 

 result which is obtained, while that of the comet's orbit is neg- 

 lected. This omission is by no means warrantable, and the 

 method can be of no manner of service even if the intervals be 

 infinitely small, and the observations perfectly correct, unless 

 the comet be many times further from the sun than the earth. 

 It might, for example, have been employed with some advantage 

 in the case of the Georgian planet, before the true nature of 

 this body was discovered. I omit, for the sake of brevity, the 

 demonstration of my assertion that the problem becomes inde- 

 terminate when the earth is supposed to describe a right line 

 with a uniform velocity, although it may be exhibited in different 

 forms; and I shall only remark, that the four lines of direction, 

 and the two portions of the orbits, are, upon this supposition, 

 tangents of one and the same parabola, of which every other 

 tangent is divided in the same proportion by the lines of direc- 

 tion. This ambiguity seems to have escaped the penetration of 

 the celebrated Lambert, notwithstanding the labour he em- 

 ployed on the problem, for the proposal, by which he attempted 

 to improve it, renders it completely indeterminate, and conse- 

 quently useless. Lalande informs us that Boscovich had 

 long ago shown the insufficiency of this method, as well as of 

 Bouguer's ; but I am not acquainted with the nature of his 

 demonstration. 



§ 24. 

 On the whole, therefore, it appears that equations of the first 

 degree are insufficient for the solution of the problem, since the 

 distance must be determined from magnitudes of the same 

 order with those which are neglected, when the motion of the 

 comet is supposed to be equable and rectilinear. 



§ 25. 

 If we assume that the chords of both orbits are divided by the 

 revolving radii in the proportion of the two intervals of time, 



