Olbers' Essay on CofneU, 419 



is capable of affording any thing like a true result ; in all other 

 cases it is totally useless. 



§ 23. 



The same remark may be applied, and for a similar reason, 

 to another problem, which has excited much attention among 

 those who have cultivated the theory of comets ; that is, having 

 four right lines given, to find a fifth that shall cut them in a 

 given proportion. Wren, Newton, Gregory, Cassini, and 

 Lambert, have given solutions of this problem ; and it has fre- 

 quently been proposed to consider the path of a comet, between 

 four observations, not remote from each other, as a right line, 

 described with an equable velocity ; and by means of this pro- 

 position to deduce, from the four observed longitudes, the 

 curtate distances of the comet from the earth. If, indeed, the 

 four given lines are not in one plane, the position of the fifth, 

 which cuts them all, is determined without any regard to the 

 proportions of the segments; so that, ifwe took the latitudes into 

 consideration, we might determine the orbit from the four ob- 

 servations, merely upon the supposition that the portion consi- 

 dered is a right line, without any regard to the velocity. The 

 position of this line would, however, require the solution of an 

 equation of the eighth degree, and in form somewhat compli- 

 cated. It would also require the same limitations as the method 

 of Bouguer, though it would be considerably more useful, for 

 the velocity of the comet is always the most unequal when its 

 motion is the most nearly rectilinear, and the reverse. It must, 

 however, be remarked, that no person seems to have made an 

 experiment of the method in question, at least with any success. 

 Even Cassini, who founded his whole theory of comets upon 

 it, never actually reduced it to practice. The method by which 

 he succeeded in determining the distance of the comet in 1729, 

 is different from this, though not very essentially, and the pro- 

 blem of Wren might have been applied to this comet, for the 

 same reason that the error of Bougueu's result was inconsi- 

 derable. Cassini indeed attempted to apply it to the comet of 

 1742, but he complains that the observations are not sufficiently 

 accurate for the purpose ; this, however, is not the true reason 



