O^U' ,)N ' THF PLANET CEKTS. 



From an hello- The heliocentric arc, which the planet has palled through in 



centric arc pad- a „[ VGll time, being thus nearly afcertained, the whole up- 

 over in a known ° . , . 

 time, its ap- proximate period is next found on a fuppofition of equal arcs 



proximate penod being paffed through in equal times; which will afford data 



is deduced;— J ° ' . . » l _ 



and thence by tor determining a tome what more accurate diitance ot the 



Kepler's law a pl ane t from the fun, by the well known law of Kepler, by 

 And the compu- ^Hich the fquare of the periodic times are analogous to the 

 tations may thus cubes of the mean diftances ot* the earth and any other planet 

 amended! * refpe&ively : an approximate diitance being thus obtained 

 may, in the next place, be fubftituted for the ajfumed diitance, 

 and the parallax of the orb be determined a fecond, and even 

 a third time in this way ; by means of which repetitions 

 an approximate period, and a correfponding approximate 

 Errors from ex- diftance, will be obtained. Thefe will vary more coniider- 

 ably from the truth the greater the diitance of the obferved 

 arc is from one of thofe two points of the orbit where the 

 planet has a mean motion ; which points are always nearer to 

 the aphelion than to the perihelion point, by a quantity which 

 depends upon the eccentricity. If therefore it fiiould fo hap- 

 pen that a new planet, at the time of itsfirft difcovery, were 

 at, or very near, its mean diitance, the whole period and 

 diitance obtained from a few of the firit obfervations would be 

 pretty accurate, 

 corrected by de- The next ftep to be taken is to determine the increments 

 terrriimng the or decrements of motion, when a number of geocentric are 



elementary . ' . . ° 



points of the changed into heliocentric places, and thus to trace the points 

 orbit, &c. i n the ecliptic where the velocity is a maximum, where it is a 



minimum, and where it is a mean. Thefe will mew where 

 the perihelion and aphelion points are, and alfo the place of 

 equated anomaly at an inftant when the equation is a maxi- 

 mum ; thefe data afford ihe means of calculating the greateft 

 equation and cone 1'ponding eccentricity ; but before they can 

 be affigned with accuracy, a confiderable time muft elapfe to 

 afford the aitronomer an opportunity of obferving a few fuc- 

 cellive oppofitions or conjunctions and ftationary points, for 

 the purpofe of correcting the approximate elements, and of 

 determining the true ftiape and pofition of the orbit, 

 determination In the mean time the geocentric latitudes, gained by obfer • 



of the obliquity vat ; on mu ft be alfo converted into heliocentric latitudes, in 



and place of the , 



nodes. order to determine the nodes or points where the two oppofite 



fides of the orbit croft the ecliptic. For doing this the analogy 



