XTO M DE Zacii's AJlrcnomlcal Ohferja'/iQtu-, 



The angle .v defines tlierefore the pofitlon of the axis and 

 the two anomalies required, the perihelial diftance being 

 _^ -= 2^:±: 2^7, lin. .v, it will be known alto by the angle .v. 



In order to find the thne the comet emplovs in runnino' its 

 anoinalies, let the perihelial dlftatice jnd: now invefl:igated^/> be 

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

 i\vept by the radius vector will be by the nature of the para- 

 bola ! PQ X OM 4- 1 SO X QAI :=. :^- ^ ^ ^^^ + ^so x OM ^ ^^^^ 



. 44 



44, r. 22 



tlie periphery of the earth's orbit is j \ 2Z \: 2p '. ~p\ 



therefore the whole area -p.lp—~— 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 v/2 : i. If the pa- 

 rabolic area -of the comet is divided by s/z it comes out 

 ^ A equal to an area that the earth -deicribes 111 



the very fame time; put therefore A equal to the time of a 

 fidereal year, we (hall recover the analogy ; the whol-e area of 

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

 parabohc area is to the time con fumed in fweeping it ; therefore 



-If , A :, j4j^-^ 3SOIMO . 7A(4l-O + 3S0)MO. ^^^ Qj^j^ 

 7 6v^2 ^ 'jip^'^z 



SM . fin. anom. PSM and OS =: SM . cof. anom. PSM ; let 

 the anomaly he — S, we have OM=:/7/ fni. ^, and OS z=:}?i cof 5; 

 therefore PO ~ p — m cof. ^. SublVitutlng we obtain 



i — ^-^ — — = which IS - — -^ =i — ■ , 



'thereby the time is found in parts of a fidereal year. 



I am, &c, 



SiPv, 



