489 



plies it to he so. The presence of animal matter is by no means con- 

 clusive; since bones from the plaster quarries at Paris still contain it. 

 Unfortunately, our geological knowledge of Guadaloupe is yet too 

 imperfect to assist in determining this question. The only positive 

 information being, that the bed in which these skeletons are found is 

 nearly an English mile in length, and that it is covered by the sea at 

 high water. 



A new Method of deducing a first Approximation to the Orbit of a 

 Comet from three Geocentric Observations. By James Ivory, A.M. 

 Communicated by Henry Brougham, Esq. F.R.S. Read February 

 17, 1814. [Phil. Trans. 1814, p. 121.] 



Although it be true that three geocentric observations are really 

 sufficient for determining the parabolic orbit of a comet, as well as 

 the elliptic orbit of a planet ; the latter problem is far the easier, be- 

 cause we can select those positions of a planet from which its helio- 

 centric places are found without any intricate calculation : but with 

 regard to comets it is far otherwise. Since their appearance is un- 

 expected, we are under the necessity of drawing our inferences from 

 those positions in which they may happen to present themselves ; and 

 it is generally extremely difficult to deduce, with accuracy, their 

 heliocentric positions from observations necessarily confined to a small 

 part of their orbit. 



In order to obtain an approximate solution, Sir Isaac Newton con- 

 sidered a small portion of the orbit as a straight line, the projection 

 of which on the plane of the ecliptic will be also straight, and the 

 parts of each will bear the same proportion to each other as the in- 

 tervals of observation. But three observations alone leave the pro- 

 blem indeterminate ; and though when four observations are employed 

 the problem is generally determinate and easily solved, it is also often 

 indeterminate even when four are employed. 



In general it may be said that no solution is free from this imper- 

 fection, in which the velocity in the orbit does not enter as a prin- 

 cipal condition, as in the methods of Boscovich, Laplace, and Le- 

 gendre. But in that of Laplace, the first and second differential co- 

 efficients of longitude arid latitude can be obtained but imperfectly, 

 and only by interpolation ; and in that of Legendre his formulae are 

 complicated, and the number of equations that require to be solved 

 render it ill adapted for general use. 



The object of the present paper is to give a new solution of the 

 problem, which, in the author's estimation, is at least as accurate as 

 any former method ; and in practice, he thinks, as commodious as 

 the nature of such a calculation can well admit. 



After detailing the particulars of this method, which from its na- 

 ture cannot admit of abridgement, the author gives various instances 

 of its successful application in discovering the orbits of the comets of 

 1769, 1781, and two comets of 1805, from observations selected by 

 Legendre for the same purpose ; and he shows, by comparison of his 



