32 



THE ORBIT OF URANUS. 



The uncorrected mean distance is deduced from the mean motion by the rela- 

 tion 



j/(l+m) 



a 



11 



We thus have 



Uncorrected mean dist. (log) 

 Action of the planets 

 Corrected lot; a 



Saturn. 



0.979496 



+ LSI 



0.979677 



Uranns. 

 1.282901 

 + 197 

 1.283098 



The following functions of the elements are derived from the preceding ele- 

 ments by well known formulfB: — 



Y (mutual inclination) 



log sin ^ y = or 



1° 57' 24.4" 

 8.232373 



log cos i y 9.9999367 



T (long, of ascending node of Saturn on Uranus) 126° 44' 51" 

 o 41 31 40 



0)' _ 323 18 21 



o' — (o = ((o) 281 46 41 



log sin (u) —9.990759 



log cos (o)) +9.309888 



sin 2((j) —0.39966 



cos 2(cj) —0.91667 



a 0.497249 



1^ 



4.04438 



The following functions of a, necessary in computing the coefficients h, are 

 derived from llunkle's Tables, published by the Smithsonian Institution: — 



