'x'5"o ^^' DE Zach's /ijlronomical Qhfervaiions^* 



The angle x defines therefore the pofltlon of the axis and 

 the t\v6 anomalies required, the perihelial diftance being 

 ptB-z^i^x 2y. (in. .V, -it will be known alfo hy the angle x. 



In order to find the time the comet employs in running its 

 anomalies, let the perihelial diftance jufl: now inveftigated^ be 

 equal to the radius of the earth's orbit, the parabolic area 

 fvvept hy the radius vector will be by the nature of the para- 



bolatPOxOM + iSOxOM^iS^-^i^^t-^^^^-^^. Now 



the ,per;phe.ry of the earth's orbit is j : zz v. 2p \~ p i 



7 



A A 2 



therefore the whole rtrea -p. l/>— — p\ It is known that the 

 velocity of a heavenly body moved in a circular path, is to 

 the velocity in a parabolic path in the ratio s/i : i . If the pa- 

 rabolic area of the comet is divided by v/a it comes out 



-^ -£3 —equal t-o an area that the earth'delcribes iii 



6V/2 ^ 



the very fame time--; put therefore A equad to the time of a 

 lidereal year, we (hall recover the atialogy ; the whale area of 

 the earth's orbit is to the time in which it is defcribed as the 

 parabolic area h to the time confumed hi fweeping it ; therefore 

 ^ P^ . A:-- (4PQ + 3S Q) ^IQ . 7A(4?Q + 3SO)MO .. ^^^ ^^^ _ ' 

 T ^ ' '" 6v^2 '• ' 72/V2 



SM . fm. anom. PSM and OS = SM . cof. anom. PSM ; let 

 the anomaly be=r^, we have OMrrw fin. (5*, and OS=zm cof. S; 

 therefore PO ~ p — m cof. I. Subllituting we obtain 



7 A (4/)— 4w cof. ^-f 3w cof. i") m fin. ^ .... 7 A (4^ — m cof. a) m fin. 

 •]2p^^2 72/)^v^2 



whereby the time is found in parts of a fidereal year. 



1..^ 



I am, &C. 



SIR, 



