Me GEORGIUM SIDVS. 321 



LET AS be = a, CS = c, ES = e t the angle ASE = #, 

 CSE = y, and ESP = z. 



IT is evident that EH : EK = : tA, = CS ES : AS- ES, 

 c e : a e j alfo, SF z: c.cof^y, SG r= a.cof,x, CF = c.Jin y y t 

 and AG = ./?, * ; alfo, the angle FCH = G AK, = ESP, = z. 



THEREFORE, FH = CE.tan,z t = cfm,y.tan y z, and GK = 

 a.Jin,x.lan,z i therefore, EH =: e c.cof,y + c.Jin,y.tan t z ) and 

 EK. =: e a.cof, x + a.ftn, x.tan, z \ therefore, c e \ a e 

 e c.cof,y + c.Jin, y.tan, z : e a.cof, x + a.Jin,x.tan,z, and 

 (c e].(e a.cof,x) + (c e).a.Jin,x.tat), z = (a e].(e c.cof,y) 

 + (a e).c.Jin, y.tan, z. This gives, 



.(ea. cof, x ) 



JL tlflj /o * -~ " 



~" /- x 7 / ^ 



c.(a e)Jin t y a.(c e),Jin,x 



Or, more conveniently for logarithms, 



c, (ae}. cofya. (ce} cof t xe.(ac} 



J.Un.% _ - 7 - r - -~ - 7 - r - -x - 



c.(ae}.fm,ya.(ce).fin, x 

 Then, by the common theorems, we have the excentricity t = 



- - - - * . the mean diftance being- = i. The 

 e . cof, za. cof, 0+z) 



aphelion and perihelion diftances are I + and i t. By their 

 means, we obtain the mean anomalies correfponding to the true 

 anomalies OSA and OSE. The difference of the mean anoma- 

 lies is to 360, as the time between the appulfes of the Planet 

 to the points A and E to the time of a fydereal revolution. 

 The fquare of a fydereal year is to the fquare of the time of 

 this revolution, as i to the cube of the Planet's mean diftance 

 from the Sun. 



This procefs gives us the following elements : 

 Mean Diftance, 19,08247 



Excentricity, 0,9006 



Periodic Time, - 83,359 Years. 



S f Mean 



