40 ON THE PERTURBATIONS OF URANUS. [2 



Sr _ ldr~ lcZ8 l8a_l_e8e _1 , .dA, 

 7 = rdt b ^~2ndt + a 2 1 -e 2 6^ * da 



i cos {i (?i< - n't + t - e') -nt-e + m} 

 i cos {i (nt- n't + e - e') - nt - e + CT'} 



where S{ denotes the whole correction of the mean longitude at the time t, 



-r- = e sin {nt + e w| + ',- sin 2 {? + e rar} nearly, 

 r ae 2 



2 TO 



-7^7 -- A- - 4 ,- 



4 z (w ') n { da 



F 1 (?.TL 1 )_ n f/oy iu,/l 

 4i(-')-^\ ( ^ 



i assuming all integral values positive and negative not including zero. 



57. By substituting in this formula the values of tn', So, Se, &c., already 

 obtained, and putting = 19'191, we find the following results corresponding 

 to the two assumed values of the mean distance. 



HYPOTHESIS I. 



a ~ a dr ^ y a rfSt 

 -8r=-j 8^-jr ,,-0-000089 

 r r de 2 ndt 



+ 0-000069 cos {nt-n't + e-e?} 



+ 0-000259 cos 2 {nt - n't + e - e'} 



+ 0-000109 cos 3 {nt-n't + e-^} 



+ 0-0000 16 cos {n't + f'-vr} 



-0-000168 cos 



+ 0-000078 cos 



-0-000049 cos 



+ 0-000209 cos {2nt - 3n't + 2e - Se' + or'}. 



