476 Reply to Mr. Barlow* s Article 



cumstance, which makes known dpriori one of the elements 

 of the orbit, introducing a new equation, it follows from it 

 that the determination of parabolic orbits of comets con- 

 duces to more equation! than unknown quantities, which 

 gives room for various methods of calculating them. After 

 having ascertained that method which ought to give the 

 greatest precision, the author enters upon the subject at full 

 length, and divides it into two pars: in the first he deter- 

 mines nearly the perihelion distance of the comet, and the 

 time of its passage by the perihelion : in the second he gives 

 the method of correcting these two elements by means of 

 three observations taken at a distance from eaoh other, and 

 he deduces all the others from them. There exists a peculiar 

 case in which the o^bit of the comet may be rigorously 

 determined : it is that case wherein the comet has been 

 observed in its two nodes : after having examined it, the 

 author gives the corrections necessary to be made in the ele- 

 ments calculated in the parabola to obtain the correspond- 

 ing elements in the ellipsis : these inquiries, applied to co- 

 mets, furnish the method of determining nearly the dura- 

 tion of their revolutions, when we have a -great number of 

 very exact observations, both before and after the passage 

 by the perihelion. The method explained has the double 

 advantage of correcting, by the number of observations, the 

 influence of their errors, and of giving the elements by a 

 rigorous analysis, simply by making the approximations to 

 fall upon those data which are given by observation. 



[To be continued.] 



LXXXIV. Reply to Mr. Barlow's Article on Floating 

 Bodies. By G. Orr, Esq., of Buckingham Place, 

 Fitzroy Square. 



To Mr. Til loch, — Sir, 

 In sending for your Magazine of March last a short essay 

 on the subject of barges, timber, &c, floating down rivers, 

 streams, or currents, it was not my intention to court a 

 paper war. But Mr. Barlow * having asserted that I did not 



* Philosophical Magazine-for April 1809, p. 300. y 



under- 



